Question

look at this diagram: if $overleftrightarrow{pr}$ and $overleftrightarrow{su}$ are parallel lines and $mangle pqt = 129^{circ}$, what is $mangle pqo$?

Explanation:

Step1: Recall angle - addition property

$\angle PQT$ and $\angle PQO$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle PQT = 129^{\circ}$ and $m\angle PQO=x$. Then $m\angle PQT + m\angle PQO=180^{\circ}$, so $x = 180^{\circ}-m\angle PQT$.

Step3: Calculate the angle measure

Substitute $m\angle PQT = 129^{\circ}$ into the formula: $x=180 - 129=51^{\circ}$.

Answer:

$51$