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 A
Find the measure of^6 RQS.
112 ◦is an exterior angle of 4 RQS. Therefore, it is supplementary to^6 RQSbecause they are a linear pair.
112 ◦+m^6 RQS= 180 ◦
m^6 RQS= 68 ◦If we draw both sets of exterior angles on the same triangle, we have the following figure:
Notice, at each vertex, the exterior angles are also vertical angles, therefore they are congruent.