Question

1. if $\angle pqr$ and $\angle sqt$ are vertical angles and $m\angle sqt = 109^\circ$, find $m\angle pqr$.

Explanation:

Step1: Recall Vertical Angles Theorem

Vertical angles are equal in measure. So, if \( \angle PQR \) and \( \angle SQT \) are vertical angles, then \( m\angle PQR = m\angle SQT \).

Step2: Substitute the Given Measure

We know that \( m\angle SQT = 109^\circ \). Using the Vertical Angles Theorem, we substitute this value into the equation from Step 1. So, \( m\angle PQR = 109^\circ \).

Answer:

\( 109^\circ \)