Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle qpr = 114^{circ}$, what is $mangle qpm$?

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles are supplementary, which means their sum is 180°. ∠QPR and ∠QPM form a linear - pair.
Let \(m\angle QPR = 114^{\circ}\) and \(m\angle QPM=x\). Then \(m\angle QPR + m\angle QPM=180^{\circ}\).

Step2: Solve for \(m\angle QPM\)

We have the equation \(114^{\circ}+x = 180^{\circ}\).
Subtract 114° from both sides: \(x=180^{\circ}- 114^{\circ}\).
\(x = 66^{\circ}\)

Answer:

66