Rule

Supplement Theorem

If two angles form a linear pair, then they are supplementary angles.
Two angles that form a linear pair

In the diagram, ∠ 1 and ∠ 2 form a linear pair. According to the theorem, the sum of the measures of these two angles is equal to 180^(∘).


m∠ 1 + m ∠ 2 = 180^(∘)

The Supplement Theorem can also be called Linear Pair Theorem.

Proof

Consider two angles that form a linear pair.

Two angles that form a linear pair

Here, ∠ 1 and ∠ 2 form a linear pair since their non-common sides are opposite rays. Moreover, the non-common sides form a straight line, which means that m∠ ABC=180^(∘). Using the Angle Addition Postulate, m∠ ABC can be written as the sum of m∠ 1 and m∠ 2. m∠ 1 + m∠ 2 = m∠ ABC ⇓ m∠ 1 + m∠ 2 = 180^(∘) The above equation implies that ∠ 1 and ∠ 2 are supplementary angles.

Exercises