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 linear - pair property

A linear - pair of angles add up to 180°. ∠PQT and ∠PQO form a linear - pair.
Let \(m\angle PQO=x\). Then \(m\angle PQT + m\angle PQO=180^{\circ}\).

Step2: Substitute the given angle value

We know that \(m\angle PQT = 129^{\circ}\). Substituting into the equation \(129^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-129^{\circ}\).
\(x = 51^{\circ}\).

Answer:

\(51^{\circ}\)