Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

m4=m1+m2

Proof:

Given: ΔPQR

To Prove: m4=m1+m2

Statement
Reason
1
ΔPQR is a triangle
Given
2
m1+m2+m3=180°
Triangle Sum Theorem
3
3 and 4 form a linear pair
Definition of linear pair.
4
3 and 4 are supplementary
If two angles form a linear pair, they are supplementary.
5
m3+m4=180°
Definition of supplementary angles.
6
m3+m4=m1+m2+m3
Statements 2, 5 and Substitution Property.
7
m4=m1+m2
Subtraction Property.