1. 7-2: Exterior Angle Theorem

2. 7-2: Exterior Angle Theorem
Exterior Angle: An angle of a triangle that forms a linear pair with one of the angles of the triangle.
Remote Interior Angles: The angles that do not form a linear pair with the exterior angle.
Remote Interior Angle
Exterior Angle

3. 7-2: Exterior Angle Theorem
Identify each exterior angle. Then, identify the remote interior angles
Note that each exterior angle at a vertex share the same interior angles
Exterior Angle
Remote Interior Angles 4
2 & 3 5
1 & 3 6 7
1 & 2 8 9

4. 7-2: Exterior Angle Theorem
Theorem 7-3 (Exterior Angle Theorem): The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles.
4 = 1 + 2
Discuss Proof 4 1 2 3

5. 7-2: Exterior Angle Theorem
If m2 = 38 and m4 = 134, what is m5?
4 = 2 + 5
134 = 38 + 5
96 = 5
If m2 = x + 17, m3 = 2x, and m6 = 101, find the value of x.
6 = 2 + 3
101 = x x
101 = 3x + 17
84 = 3x
28 = x

6. 7-2: Exterior Angle Theorem
Your Turn
What is 1 if m3 = 46 and m5 = 96?
142
If m2 = 3x, m3 = x + 34, and m6 = 98, find the value of x. Then, find m3.
x = 16
m3 = 50

7. 7-2: Exterior Angle Theorem
Two “common sense” theorems are derived from the Exterior Angle Theorem.
Theorem 7-4: The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles.
Theorem 7-5: If a triangle has one right angle, then the other two angles must be acute.

8. 7-2: Exterior Angle Theorem
Assignment
Worksheet #7-2