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Common Core Standard  G.CO.9
video tutorial  interior angle measure
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​How do you find the interior angle measure of a triangle?  The sum of these angle measures equals 180 degrees. 

​You can use this fact in order to find missing angles of a triangle. Let's look at two examples from the video.

Example 1. Find the missing angle in following triangle.

Step 1. 70 + 32 + x =180   
Step 2. 102 + x = 180                  
Step 3. x = 78

Example 2. Find the missing angle in the following triangle.

Step 1. 90 + 48 + x = 180
Step 2. 138 + x = 180
Step 3. x = 42



Interior Angle measure of a Triangle

Triangle angles 32 and 70 degrees
Triangle with 48 and 90 degree angles
​70°
​32°
​48°
​90°
X
X
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Interior Angles Definition

​An Interior Angle of a triangle is the angle formed inside the triangle at the vertex formed by two adjacent sides.

The interior angles of a triangle always add up to 180 degrees.



two lines cut by transversal
interior angles of a triangle highlighted
When two lines are cut by a third line known as a transversal, then the four angles formed between the lines are called Interior Angles.

Interior angles are highlighted
​What is the relationship between the interior and exterior angles of a triangle?

An interior angle and its corresponding exterior angle create a linear pair and have a sum 180°.

Each vertex of a polygon has one interior angle and one exterior angle.

interior and exterior angles of a triangle
The sum of the angles inside a triangle equals 180 degrees.

Finding the interior angle measure of a triangle

Interior Angle
Exterior Angle
                  Given:  a||b          

Statement

​1.  a||b

2.  <4 + <3 + <5 =180

3. <4  = <1

4. <5  = <2

5.  <1 + <3 + <2 = 180

6.  <1 + <2 + <3 = 180


Reason

1.  Given

2.  Definition of Linear Pair

3. a||b therefore Alternate Interior <   are equal

4.  a||b therefore Alternate Interior < are equal

5. Substitution Property of equality

6.  Commutative Property of equality


triangle created by two transversals and parallel lines
A triangle is created by two transversals intersecting parallel lines.

Prove: <1 + <2 + <3 = 180

Proof the interior angles of a triangle equal 180 degrees

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Remote Interior Angles ( highlighted in picture below)  The two angles inside the triangle that do not share a vertex with the exterior angle are called the remote interior angles. 

Here is the interesting part, if you add the angle measure of the two remote angles,it will equal the measure of the exterior angle. 

Remote∠1 + Remote∠2 = Exterior∠ 3