http://www.ck12.org Chapter 4. Triangles and Congruence
TABLE4.2:
Statement Reason- 4 ABCwith exterior angle^6 ACD Given
2.m^6 A+m^6 B+m^6 ACB= 180 ◦ Triangle Sum Theorem
3.m^6 ACB+m^6 ACD= 180 ◦ Linear Pair Postulate
4.m^6 A+m^6 B+m^6 ACB=m^6 ACB+m^6 ACD Transitive PoE
5.m^6 A+m^6 B=m^6 ACD Subtraction PoE
Example 8:Findm^6 C.
Solution:Using the Exterior Angle Theorem,m^6 C+ 16 ◦= 121 ◦. Subtracting 16◦from both sides,m^6 C= 105 ◦.
It is important to note that if you forget the Exterior Angle Theorem, you can do this problem just like we solved
Example 7.
Example 9:Algebra ConnectionFind the value ofxand the measure of each angle.
Solution: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.