Question

look at this diagram: if $overleftrightarrow{mo}$ and $overleftrightarrow{pr}$ are parallel lines and $mangle onq = 52^{circ}$, what is $mangle mnq$?

Explanation:

Step1: Recall linear - pair property

The sum of angles in a linear - pair is 180°. $\angle ONQ$ and $\angle MNQ$ form a linear - pair.

Step2: Set up the equation

Let $m\angle MNQ=x$. Then $m\angle ONQ + x=180^{\circ}$.

Step3: Substitute the given angle value

Since $m\angle ONQ = 52^{\circ}$, we have $52^{\circ}+x = 180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}-52^{\circ}=128^{\circ}$.

Answer:

$128$