# What Is The Interior Of An Angle

## Definition of INTERIOR ANGLE

Recent Web-based illustrations Both constructions are three-dimensional, yet their geometries are vastly different: Their floor plans are distinct, the curvature of their exteriors is different, and the angles of their interiors are varied as well. —Quanta Magazine, published on April 9, 2018 Both constructions are three-dimensional, yet their geometries are vastly different: Their floor plans are distinct, the curvature of their exteriors is different, and the angles of their interiors are varied as well.

—Quanta Magazine, published on the 31st of October, 2019.

—Quanta Magazine, published on April 9, 2018 Both constructions are three-dimensional, yet their geometries are vastly different: Their floor plans are distinct, the curvature of their exteriors is different, and the angles of their interiors are varied as well.

—Quanta Magazine, April 9, 2018Both constructions are three-dimensional, however their geometry is vastly different from one another: Their floor plans are distinct, the curvature of their exteriors is different, and the angles of their interiors are varied as well.

—Quanta Magazine, published on January 6, 2015 Following are some sample sentences that were automatically generated from various internet news sources to reflect current use of the word ‘interior angle.’ It is not the opinion of Merriam-Webster or its editors that the viewpoints stated in the examples are correct.

## Interior and Exterior of an Angle

The inside and exterior of an angle are discussed in this section. If the angle ABC is drawn with two arms BA and BC, the shaded part between them can be stretched forever. This region of the angle is referred to as the inside of the angle. X is a point that is within the interior of the right angle. The point Y is located on the outside of the oblique angle. The angle is defined by the point Z. The inner angle in the above illustration is denoted by the number 1 since it falls between the two arms.

At the point where two rays come together, two angles are generated – one is called an internal angle, and the other is called an exterior angle. It is not the length of the arms that determines the magnitude of an angle, but the amount of turn or rotation that occurs between two arms that does.

### Here ∠a is greater than ∠b, ∠b is greater than ∠c.

●Angle. Angles have two sides: the interior and the outside. A protractor is used to measure an angle. Angles are classified into several categories. Angles in pairs are referred to as angles. Creating a bisecting angle. Compass construction is used in the construction of angles. Angles worksheet to print off and complete. Angles are the subject of this Geometry Practice Test.

Let us know what you think about what you’ve just read! Please leave a remark in the section provided below. You may either ask a question or respond to a question. Were you unable to locate what you were searching for? Alternatively, you may choose to obtain further information on Math Only Math. To locate what you’re looking for, use this Google Search.

## Interior Angles – Definition, Meaning, Theorem, Examples

Intersections of two parallel lines intersected by a transversal are also referred to as interior angles. Similarly, the angles that exist in the region bordered by two parallel lines that are intersected by a transversal are also referred to as interior angles.

 1 What are Interior Angles? 2 Types of Interior Angles 3 Interior Angles of a Triangle 4 Sum of Interior Angles Formula 5 Finding an Unknown Interior Angle 6 Interior Angles of Polygons 7 FAQs on Interior Angles

## What are Interior Angles?

Interior angles can be generated in two different methods in geometry. One occurs when parallel lines are cut by a transversal, whereas the other occurs when parallel lines are not cut by a transversal. Angles are classified into distinct categories based on the measures that they possess. There are additional sorts of angles that are referred to as pair angles since they must exist in pairs in order to display a specific attribute. Pair angles are defined as One type of angle is the interior angle.

• Angles within a Polygon:Interior angles are those angles that are contained within a form, which is often an apolygon shape. Figure (a) below shows that the internal angles (a, b, and c) are all the same size. Interior Angles of Parallel Lines (also known as internal angles of parallel lines): Intersections of two parallel lines by a transversal are also known as interior angles, and the angles that fall within the region contained by two parallel lines are also known as interior angles. (b) In the image below, the letters (L 1) and (L 2) are parallel, and the letter L is the transversal. The angles 1, 2, 3, and 4 are all internal angles
• The angles 1, 2, 3, and 4 are all exterior angles.

## Types of Interior Angles

There are two sorts of interior angles that are generated when two straight lines are sliced by a transversal, and they are alternate interior angles and co-interior angles. Alternate interior angles are the most common type of interior angle.

• Intersection of Two Parallel Lines by a Transversal: When two parallel lines are crossed by a transversal, alternate interior angles are generated. This non-adjacent pair of angles is produced on the transversal’s opposing sides, and they are not next to one another. The pairs of alternate interior angles shown in the preceding image (b) are 1 and 3, 2 and 4, and 3 and 5. If two parallel lines are intersected by a transversal, the lengths of the lines are equal. Co-InteriorAngles: These angles are a pair of non-adjacent internal angles on the same side of the transversal that are not contiguous to one another. The pairs of co-interior angles shown in the preceding image (b) are numbered 1 and 4, 2 and 3, and 3 and 4. They are also known as same-side internal angles or consecutive interior angles, depending on how they are formed. Due to the fact that the total of two co-interior angles equals 180o, they also form a pair of supplementary angles.

## Interior Angles of a Triangle

At each vertex of a triangle, there are three internal angles to be considered. The total of all of these internal angles is always 180° in each case. The intersection of the bisectors of these angles is known as the incenter. In a triangle, because the total of its internal angles equals 180°, there is only one possibleright angleorrobtuse angle that can be formed in each triangle. A triangle with all three acute interior angles is known as an acute triangle, a triangle with one obtuse interior angle is known as an obtuse triangle, and a triangle with one right angled interior angle is known as aright angled triangle.

## Sum of Interior Angles Formula

For example, from the smallest polygon, such as a triangle, to an endlessly complicated polygon with n sides, such as an octagon, all of the sides of the polygon combine to form a vertices, and each vertices has an interior and exterior angle. According to the angle sum theorem, the sum of all three internal angles of a triangle equals 180° when all three angles are equal. The total of the internal angles of every polygon may be calculated by multiplying the number of sides by two less than the number of sides times 180°.

A polygon is defined as follows: S = sum of internal angles n = total number of sides of the polygon When we apply this formula to a triangle, we obtain the following result: S = (n 2) x 180°S = (3 x 2) x 180°S = (1 x 180°S = 180°S = 1 x 180°S = 180° The sum of the internal angles of polygons is determined using the same method as the sum of their exterior angles:

See also:  How Much To Hire An Interior Designer
Polygon Number of sides, n Sum of Interior Angles, S
Triangle 3 180(3-2) = 180°
Quadrilateral 4 180(4-2) = 360°
Pentagon 5 180(5-2) = 540°
Hexagon 6 180(6-2) = 720°
Heptagon 7 180(7-2) = 900°
Octagon 8 180(8-2) = 1080°
Nonagon 9 180(9-2) = 1260°
Decagon 10 180(10-2) = 1440°

## Finding an Unknown Interior Angle

Using the “Sum of Interior Angles Formula,” we may get the interior angle of a polygon that is unknown. Consider the following example in order to determine the angle x that is missing from the following hexagon. The total of the internal angles of a hexagon is 720° when the interior angles of a polygon table are given in the preceding paragraph. Two of the hexagon’s internal angles are right angles, as seen in the diagram above. As a result, we have the following equation: 90° plus 90° plus 140° plus 150° plus 130° plus x Equals 720° Let’s see if we can figure out what x is by solving this.

## Interior Angles of Polygons

When all of a polygon’s sides and angles are congruent, the polygon is said to be an irregular polygon. Some instances of regular polygons are shown below. For a polygon with ‘n’ sides, we already know that the total of the interior angles of a polygon is given by the formula 180(n-2)°. In a regular polygon with ‘n’ sides/vertices, there are ‘n’ angles to be found. In a regular polygon, because all of the interior angles are equal, each interior angle may be calculated by dividing the total of the angles by the number of sides of that polygon.

Let us try to use this formula to get the internal angle of a regular pentagon and see how it turns out.

In a regular pentagon, the interior angles may be calculated by dividing by n and using the following formula: ((180(n-2))/n° = ((180(5-2))/5)°= (180 (3)/5 = 540/5= 108° As a result, the internal angle of a regular pentagon is equal to 108°.

Regular Polygon Sum of Interior Angles, S Measurement of each interior angle((180(n-2))/n)°
Triangle 180(3-2) = 180° 180/3 = 60°, Here n = 3
Square 180(4-2) = 360° 360/4 = 90°, Here n = 4
Pentagon 180(5-2) = 540° 540/5 = 108°, Here n = 5
Hexagon 180(6-2) = 720° 720/6 = 120°, Here n = 6
Heptagon 180(7-2) = 900° 900/7 = 128.57°, Here n = 7
Octagon 180(8-2) = 1080° 1080/8 = 135°, Here n = 8
Nonagon 180(9-2) = 1260° 1260/9 = 140°, Here n = 9
Decagon 180(10-2) = 1440° 1440/10 = 144°, Here n = 10

### Related Articles on Interior Angles

See the pages that follow for further information on interior angles.

• Vertical Angles
• Alternate Angles
• Alternate Exterior Angles
• Same Side Interior Angles
• Interior Angles of Polygon Calculator
• Vertical Angles
• Vertical Angle

Important Points to Keep in Mind When analyzing interior angles, the following are some important aspects to keep in mind:

• A polygon with n sides can have its inner angles added together using the formula 180(n-2)°
• This can be done using the following formula: For any interior angle of a regular polygon with a certain number of sides, the formula ((180(n-2))° may be used to compute it. A transversal intersecting two parallel lines, according to the alternative interior angles theorem, produces alternate interior angles that are identical for each pair of adjacent alternate interior angles. If, on the other hand, a transversal intersects two lines in such a way that a pair of internal angles is equal, the two lines are said to be parallel. If a transversal intersects two parallel lines, the co-interior angles theorem states that each pair of co-interior angles is supplementary (their total is 180°) and that each pair of co-interior angles is supplementary. When a transversal intersects two lines in a such that a pair of co-interior angles are supplementary, the lines are said to be parallel.

## Interior Angles Examples

1. Example 1: In the accompanying diagram, get the internal angle at vertex B by using the formula. Solution: Because the number of sides of the given polygon is n = 6, it is classified as a hexagonal polygon (Hexagon has 6 sides). This polygon has 720° as its sum of internal angles since its n-2)o.= 180(6-2)= 180(4-2)o. = 180(6-2)= 180 4 = 720° Knowing that the total of all the internal angles in this polygon equals 720°, we may proceed to the next step. In the following polygon, the total of all the angles is as follows:A + B + C + D + E + F= (x – 60) + (x – 20) + 110 + 120 + 130 + (x – 40)= 3x+ 240 Now, we’ll put this total equal to 720 and work out what the value of x is. 3x+ 240 = 7203x = 480x = 480/3 = 160 3x+ 240 = 7203x = 480 Let’s try to locate B now. In this case, B = (x – 20)° = (160 – 20)° = 140°. The internal angle at vertex B is thus b=140°
2. Example 2: In the accompanying picture, MN || OP and ON || PQ are represented by the letters MN and ON respectively. If MNO=55°, then determine the value of OPQ. Solution: We will make the lines in the given figure longer by extending them. MN || OP is a transversal in this case, and ON is also a transversal. As a result, the angles 55° and x° are co-interior angles, and as such, they are supplementary (by co-interior angle theorem). as an example:55 degrees plus x degrees equals 180 degreesx degrees equals 180 degrees less 55 degrees equals 125 degrees ON || PQ and OP are both transversals once more. As a result, x° and OPQ are equivalent angles, and as a result, they are equal. For example, OPQ = x=125°, which results in OPQ=125°.

Continue to the next slide proceed to the next slide Simple graphics might help you break through difficult topics. Math will no longer be a difficult topic for you, especially if you visualize the concepts and grasp them as a result. Schedule a No-Obligation Trial Class.

## FAQs on Interior Angles

Interior angles are those that are found within the boundaries of a polygon. The internal angles of a triangle, for example, are three. Interior angles may also be defined as “angles confined in the interior area of two parallel lines when they are crossed by a transversal,” which is another way of saying it.

### How to Find the Sum of Interior Angles?

It is possible to calculate the sum of interior angles in a polygon using the formula 180(n-2)°, where n is the number of sides in a polygon. When calculating the sum of interior angles of a quadrilateral, we may substitute n with 4 in the formula to get the result. We will have 180(4-2)°= 360° as a result.

### What is the Sum of the Interior Angles of a Heptagon?

A heptagon is a polygon that has seven sides and seven angles on each side.

900° is equivalent to 180(7-2)° because the total of all the internal angles of a heptagon equals 180(7-2)°. This results in a heptagon’s internal angles adding up to an impressive 900 degrees.

### What is the Sum of the Measures of the Interior Angles of a 27-Gon?

It is 180(27-2)° when the total of the measurements of the inner angles of a 27-gon is calculated. It is equivalent to 180 x 25, which is 4500° in radians.

### How to Solve Same Side Interior Angles?

When two parallel lines are cut by a transversal, the interior angles on the same side of the lines are additional. This implies that their total is 180 degrees. As a result, in order to solve such angles, we will make use of this characteristic and determine the missing value.

### What is the Sum of the Interior Angles of a Polygon?

By using the formula 180(n-2)°, it is possible to find out how many internal angles there are in a polygon with n sides. It aids in the calculation of the entire sum of all the angles of a polygon, regardless of whether it is a regular polygon or an irregular polygon. We can also check the angle sum property with the help of this formula as well. When you add up all of the interior angles of a triangle, you get 180o, when you add up the internal angles of a quadrilateral, and so on.

See also:  How Long Does Interior Design School Take

### What is the Sum of the Interior Angles of a Triangle?

To compute the sum of the interior angles of a triangle, we will use the sum of internal angles formula S = 180(n-2)°, where n is the number of sides of a polygon and S is the sum of inner angles formula. Because the triangle has three sides, the number n equals three. As a result, 180(n-2)° = 180(3-2)° = 180° is the sum. As a result, the total of the internal angles of a triangle is equal to 180 degrees.

### What is the Sum of Interior Angles of a Hexagon?

To find the sum of the interior angles of a hexagon, we’ll use the sum of internal angles formula S = 180(n-2)°, where n is the number of sides in a polygon and is the number of sides in a hexagon. Because the hexagon has six sides, the number n equals six. As a result, the total is 180(n-2)° = 180(6-2)° = 180 4 = 720° (180(n-2)°). As a result, the total of the inner angles of a hexagon equals 720 degrees.

### How Many Interior Angles Does an Octagon Have?

An octagon has eight sides, and as a result, it has eight angles on the inside. In an octagon, the total of the eight inside angles is 1080 degrees.

### What is the Sum of all Interior Angles of a Pentagon?

To find the sum of the interior angles of a pentagon, we’ll use the sum of internal angles formula S = 180(n-2)°, where n is the number of sides in a polygon and is the number of sides in a pentagon. The number n is 5 in this case since the pentagon has 5 sides. As a result, 180(n-2)° = 180(5-2)° = 180 3 = 540° is obtained. As a result, the total of the inner angles of a pentagon is equal to 540 degrees.

## Definition of interior angle

This indicates the grade level of the word based on its difficulty. This indicates the grade level of the word based on its difficulty. nounGeometry. an angle produced between two parallel lines by the intersection of a third line with the first two an angle created by two neighboring sides of a polygon within the polygon EVALUATE YOUR KNOWLEDGE OF AFFECT AND EFFECT VERSUS AFFECT! In effect, this exam will determine whether or not you possess the necessary abilities to distinguish between the terms “affect” and “effect.” Despite the wet weather, I was in high spirits on the day of my graduation celebrations.

## Origin ofinterior angle

The first written document dates back to 1750–60.

## Words nearbyinterior angle

Interim denture, Interim Standard Atmosphere, interinsurance, interionic, interior, interior angle, interior decoration, interior decorator, interior design, interior designer, interior drainageDictionary.com provides a comprehensive list of terms and definitions for interim denture, Interim Standard Atmosphere, interinsurance, interionic, interior, interior angle, interior decoration, interior decorator, interior design, interior designer, and interior drainage.

Unabridged Random House, Inc. 2022, based on the Random House Unabridged Dictionary, Random House, Inc.

## How to useinterior anglein a sentence

• In each of the families, there is a parameter that can be adjusted in an unlimited number of ways to make some interior angles smaller and others proportionally bigger while still keeping the ability to tile space. The gunman appears to have fired the shot through the glass, according to the internal footage. One of its most senior officers is currently serving as Baghad’s minister of the interior. I was asked to do this Hemingway part with the white stubble by Brazakka, my boat’s skipper, and he specifically requested the hero viewpoint.
• As more than 300 police motorbikes from dozens of jurisdictions drove by Justin, he peered through the gloomy inner window. In recent weeks, Isaacs has returned from the New Mexico desert, where he was filming interior sequences for a new television mini-series called Dig. The interior of the omnibuses was ornamented with a life-size replica of Mrs. Charmington herself
• Every room had some sort of water feature, whether it was a small fountain in the center or four smaller ones arranged in a circle around the space. The remaining work is accomplished by removing two higher and four lower teeth and replacing them with fake ones at the proper angle. I don’t know much about the interior design of Kullak’s conservatory because I only attended his own classes
• Yet, Intense contrast between the wide street and the contained stuffiness of the gloomy and crammed interior.

## British Dictionary definitions forinterior angle

Any of the four angles formed by a transversal that reside inside the region between two crossed lines is referred to as an angle of a polygon enclosed between two adjacent sides. Complete Unabridged Digital Edition of the Collins English Dictionary, published in 2012. William Collins Sons Co. Ltd. was established in 1979 and 1986. In 1998, HarperCollinsPublishers published the following books: 2000, 2003, 2005, 2006, 2007, 2009, and 2012.

## Scientific definitions forinterior angle

When two straight lines are crossed by a third straight line, any of the four angles created inside these two straight lines can be used. An angle produced by two adjacent sides of a polygon that is contained inside the polygon is called a right angle. Examine the outside aspect. The American Heritage® Science Dictionary is a resource for those interested in science. The year 2011 is the year of the copyright. Houghton Mifflin Harcourt Publishing Company is the publisher of this book. All intellectual property rights are retained.

## What Are Interior Angles? – Definition & Examples

Whenever Tashmina was a small girl, she dreamed of growing up and decorating the interiors of people’s houses. She enjoyed rearranging the furniture in her room, including the bed, the dresser, the bookcases, and her stuffed animals. When she was older, she pursued a career in interior design by enrolling in courses. When Tom was younger, he wished to contribute to the preservation of national parks, lakes, and rivers. When he grew up, he began working for the United States Department of the Interior (DOI).

1. Interior?
2. Consider the implications of this.
3. The Department of the Interior is in charge of the parks that are located within the county.
4. Angles and forms have an inner and an outside, just as your house has an inside and an outside (interior and exterior).
5. An internal angle can be found in any shape or design when two lines come together.
6. The internal angles of a rectangle are equal to the number of corners it possesses.
7. Because a hexagon has six interior angles, it has six interior angles.

## Internal and external angles – Wikipedia

The term “interior angle” links to this page. See Transversal line for interior angles that are on the same side of the transversal as the transversal line. Angles both internally and outside In geometry, anangleof apolygonis created by two sides of a polygon that have the same terminus as one another. This angle is referred to as aninteriorangle(orinternal angle) for a simple(non-self-intersecting) polygon, regardless of whether it is convex or non-convex. If a point inside the angle is located within the interior of the polygon, the angle is referred to as aninteriorangle(orinternal angle).

The term “convex polygon” refers to a polygon whose internal angles are all fewer than 180 degrees (radians).

The opposite of this is anexteriorangle(also known as anexternal angleorturning angle), which is generated by one side of a basic polygon and a line drawn from the opposite side.: pp. 261-264

## Properties

• A vertex’s internal angle and its external angle add up to 180 degrees
• The total of the internal and external angles of a vertex is radians (180°). For a basic polygon with only one side, the total of all of its internal angles is (n –2) radians or 180(n –2) degrees, where n is the number of sides. Mathematical induction may be used to verify the following formula: Begin with a triangle, for which the angle total is 180°, and then replace one side with two sides that are joined at another vertex, and so on. The sum of the external angles of any simple convex or non-convex polygon, if only one of the two external angles is assumed at each vertex, is 2 radians (360°)
• If only one of the two external angles is assumed at each vertex, the sum of the external angles of any simple convex or non-convex polygon is 2 radians (360°)
• A vertex’s exterior angle is unaffected by which side is extended first: the two exterior angles that may be created at a vertices by extending alternately one side and the other are vertical angles, and hence have the same measure.
See also:  How Much To Replace Interior Door

## Extension to crossed polygons

By employing the notion of directed angles, it is possible to apply the inner angle concept to cross-sectioned polygons such as star polygons in a consistent manner. A closed polygon with a total of n vertices and a strictly positive integerk is the number of total (360°) revolutions one would make by walking around the perimeter of the polygon, in degrees, is given by 180(n –2 k)°, where n is the number of vertices and k is the number of strictly positive integers that one would make by walking around the perimeter.

When walking around the perimeter of an ordinary convex polygon (or a concave polygon), for example, k= 1, because the exterior angle sum is 360°, and traveling around the perimeter requires just one complete rotation.

## References

• A generic formula for the interior angles of a triangle
• A formula for the interior angle sum of polygons In this Java exercise, the interior angle sum formula for simple closed polygons is extended to include crossing (complex) polygons, and the result is displayed interactively.

## Interior Angles of a Polygon (13 Step-by-Step Examples!)

Do you have trouble figuring out how to get the internal angles of a polygon? In this geometry lesson, you will learn just that. Jenn, Founder Calcworkshop ®, 15+ Years Experience (LicensedCertified Teacher)You have come to the correct spot because that is exactly what you will learn in today’s geometry lesson. Let’s get started right away!

## Interior Angles

What if I told you that triangles play a key role in determining how to aggregate all of the inner angles of any convex polygon? Recall that a convex polygon does not have any angles that point inward, but a concave polygon creates something that appears to be a cave, with angles pointing inward into the interior of the polygon. Regular polygons are also those that are both equilateral (all sides are congruent) and equiangular (all angles are congruent) (all angles are congruent). Let’s start with a polygon of any size and draw diagonals from one vertex to the other.

• And the total of the internal angles is determined by the number of triangles that may be constructed.
• How?
• As Math is Funnicely points out, this means that every time we add a side, we are adding another 180° to the total, which is what we want.
• (where n is the number of sides on which the polygon is formed) The formula for each of the most frequent polygons is depicted in the chart to the right (triangle, quadrilateral, pentagon, hexagon, etc.).

Polygon Chart You’ll discover how to achieve this by watching the video below, which outlines the steps to take. Formula for the Interior Angle

## Exterior Angles

What’s more, did you know that when you have one angle at each vertex, the total of the measurements of the outer angles equals 360 degrees? As a result, if we have a regular polygon, the measure of each outside angle is equal to 360°/n degrees. In the case of a regular pentagon (5-sided polygon with equal angles and sides), each exterior angle is equal to the quotient of 360 degrees and the number of sides as stated in the table below. Angles on the outside are added together. You’ll learn how to do the following things in the video below:

1. Calculate the sum of interior angles for a variety of polygonal shapes. Find the measure of each interior and exterior angle for a regular polygon
2. You are given the measure of one exterior or interior angle of a regular polygon
3. You must determine the number of sides the polygon has. Find the measures of unknown angles for a polygon using our new formulas and properties

## Video – LessonExamples

• Angles of Polygons: An Introduction to the Video
• In this section, we will discuss formulas for calculating the total angle sum of a polygon’s inner and exterior angles. Members-Only Content
• Exclusive Content for Members Only
• Experiment with regular polygons to find the total of the interior angles and the measure of each interior and exterior angle (Examples 1–5). 00:12:01– Calculate the sum of the interior angles and the measure of each interior and exterior angle (Examples 1–5). Experiment with the number of sides of a regular polygon given an exterior angle (Examples 6-8)
• 00:23:37– Determine the number of sides of a regular polygon given an external angle
• 00:26:57– Given an interior angle of a regular polygon, determine the number of sides (Examples 9-11)
• 00:26:57– Given an interior angle of a regular polygon, find the number of sides (Examples 9-11)
• A method for finding the interior angles of an irregular polygon (Example12)
• 00:33:54– A method for finding the internal angles of an irregular polygon
• In the provided polygon (Example13), 00:38:04 is the time to find all of the unknown angles. Questions and solutions for practice problems with detailed step-by-step solutions
• Chapter tests with video solutions

With your membership, you’ll get access to all of the courses as well as over 450 HD videos. Plans are available on a monthly and yearly basis. Now is the time to get my subscription.

## Triangle Interior Exterior Angles – Maple Help

Triangles are made up of two angles: the inside angle and the outside angle.

 Main Concept Aninterior angleof a polygon is formed by two sides of a polygon that share an endpoint. A shape has one internal angle per vertex . For atriangle, an interior angle is the angle between any two of the triangle’s three sides.Anexterior angleof a polygon is any of the angles formed by the intersection of one of the polygon’s sides with a line extended from an adjacent side.Properties:- The sum of the interior angles of a triangle is equal to 180 degrees.- The sum of the exterior angles of a triangle is equal to 360 degrees.
 Instructions The plot below shows a visual representation of the properties mentioned above, namely that the interior and exterior angles of the triangle add to 180 and 360 degrees respectively.Choose either interior angles or exterior angles. Drag the red point to change the angles of the triangle and move the slider from left to right to see the proofs in motion.Interior Angles:The interior angles form a semi-circle (180 degrees).Exterior Angles:The exterior angles form a full circle (360 degrees).

The following slide will animate the proof:

## Consecutive Interior Angles Theorem

An angle pair on one side of a transversal that is contained inside two lines is referred to as a pair of successive internal angles when two lines are cut by a transversal. When two lines are severed by a transversal, a transversal is referred to as a transversal. The angles 3 and 5 in the illustration are successive internal angles. Angles 4 and 6 are also successive internal angles, as are angles 5 and 6.

### Consecutive Interior Angles Theorem

When a transversal is used to intersect two parallel lines, the pairs of successive interior angles that are generated are known as additional internal angles. Proof: Given that kl is a transversal verb, Clearly demonstrate that numbers 3 and 5 are supplementary and that numbers 4 and 6 are supplementary.

 Statement Reason 1 k∥l,tis a traversal. Given 2 ∠1and∠3form a linear pair and∠2and∠4form a linear pair. Definition oflinear pair 3 ∠1and∠3are supplementarym∠1+m∠3=180°∠2and∠4aresupplementarym∠2+m∠4=180° Supplement Postulate 4 ∠1≅∠5and∠2≅∠6 Corresponding Angles Theorem 5 ∠3and∠5are supplementary∠4and∠6are supplementary. Substitution Property