Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle opr = 136^{circ}$, what is $mangle qpr?$

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the angles in a linear pair is 180°. ∠OPR and ∠QPR form a linear pair.
Let \(m\angle QPR=x\). We know that \(m\angle OPR + m\angle QPR=180^{\circ}\).

Step2: Substitute the given value

Given \(m\angle OPR = 136^{\circ}\), we substitute into the equation \(136^{\circ}+x = 180^{\circ}\).
Then \(x=180^{\circ}- 136^{\circ}\).

Step3: Calculate the angle measure

\(x = 44^{\circ}\).

Answer:

44