Rule

Linear Pair Theorem

When two angles form a linear pair, they are supplementary.
A linear pair

Based on the diagram, the following equality holds true.


m∠ A + m∠ B = 180^(∘)

This theorem is also known as the Supplement Theorem.

Proof

Linear Pair Theorem

Consider two angles that form a linear pair. These angles are adjacent and form a straight angle.

A linear pair

By the Angle Addition Postulate, we know that the measure of the angle formed by ∠ A and ∠ B is equal to the sum of the measures of ∠ A and ∠ B. However, ∠ A and ∠ B form a straight angle, which has a measure of 180^(∘). This gives us the required equality.


m∠ A + m∠ B = 180^(∘)

Exercises