Consider that the two given angles form a linear pair.
m∠ LPM=80
Practice makes perfect
The diagram of a game timer is given below.
We see that ∠ LPM and ∠ LPQ form a straight angle. This means that the measures of these angles add up to 180^(∘). Let's use this fact to first find x.
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 Supplementary Theorem can also be called Linear Pair Theorem. We can prove this theorem by considering 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.
