Question

qs bisects ∠pqr and m∠rqs = 71°. find m∠pqs and m∠pqr. diagram: p, q, r, s with q as vertex, pq, sq, rq as rays m∠pqs = □° m∠pqr = □°

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, if \( \overrightarrow{QS} \) bisects \( \angle PQR \), then \( \angle PQS = \angle RQS \).
Given \( m\angle RQS = 71^\circ \), so \( m\angle PQS = 71^\circ \).

Step2: Calculate \( m\angle PQR \)

Since \( \angle PQR = \angle PQS + \angle RQS \), and both \( \angle PQS \) and \( \angle RQS \) are \( 71^\circ \), we have \( m\angle PQR = 71^\circ + 71^\circ = 142^\circ \).

Answer:

\( m\angle PQS = \boldsymbol{71}^\circ \)
\( m\angle PQR = \boldsymbol{142}^\circ \)