Question

look at this diagram: if line st and line qu are parallel lines and m∠pou = 122°, what is m∠sqp?

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles is supplementary, which means the sum of the measures of two angles in a linear - pair is 180°.
Let \(\angle PQR = 122^{\circ}\) and \(\angle SQR\) be the angle we want to find. Since \(\angle PQR\) and \(\angle SQR\) form a linear - pair, we have the equation \(\angle PQR+\angle SQR = 180^{\circ}\).

Step2: Solve for \(\angle SQR\)

We can rewrite the equation as \(\angle SQR=180^{\circ}-\angle PQR\).
Substitute \(\angle PQR = 122^{\circ}\) into the equation: \(\angle SQR=180 - 122\).
\(\angle SQR = 58^{\circ}\)

Answer:

\(58^{\circ}\)