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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.

m ∠ 4 = m ∠ 1 + m ∠ 2

Proof:

Given: Δ P Q R

To Prove: m ∠ 4 = m ∠ 1 + m ∠ 2

Statement
Reason
1
Δ P Q R is a triangle
Given
2
m ∠ 1 + m ∠ 2 + m ∠ 3 = 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
m ∠ 3 + m ∠ 4 = 180 °
Definition of supplementary angles.
6
m ∠ 3 + m ∠ 4 = m ∠ 1 + m ∠ 2 + m ∠ 3
Statements 2, 5 and Substitution Property.
7
m ∠ 4 = m ∠ 1 + m ∠ 2
Subtraction Property.