CK-12 Geometry-Concepts

4.2. Exterior Angles Theorems http://www.ck12.org

2. Findm^6 C.


3. Find the value ofxand the measure of each angle.

Answers:

1. Set up an equation using the Exterior Angle Theorem.m^6 A+ 79 ◦= 115 ◦. Therefore,m^6 A= 36 ◦.


2. Using the Exterior Angle Theorem,m^6 C+ 16 ◦= 121 ◦. Subtracting 16◦from both sides,m^6 C= 105 ◦.


3. Set up an equation using the Exterior Angle Theorem.

( 4 x+ 2 )◦+( 2 x− 9 )◦= ( 5 x+ 13 )◦

↑ ↗ ↑

interior angles exterior angle

( 6 x− 7 )◦= ( 5 x+ 13 )◦

x= 20 ◦

Substituting 20◦back in forx, the two interior angles are( 4 ( 20 )+ 2 )◦= 82 ◦and( 2 ( 20 )− 9 )◦= 31 ◦. The exterior
angle is( 5 ( 20 )+ 13 )◦= 113 ◦. Double-checking our work, notice that 82◦+ 31 ◦= 113 ◦. If we had done the problem
incorrectly, this check would not have worked.

Interactive Practice