Consider that the two given angles form a linear pair.
m∠LPM=80
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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.
