Question

qs bisects ∠pqr and m∠pqr = 119°. find m∠pqs and m∠rqs.
diagram: angle with vertex q, rays qp, qs, qr; qp and qs form one angle, qs and qr form another, with qs bisecting ∠pqr

m∠pqs = □°

m∠rqs = □°

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( \overrightarrow{QS} \) bisecting \( \angle PQR \) means \( m\angle PQS = m\angle RQS \) and \( m\angle PQS + m\angle RQS = m\angle PQR \).

Step2: Calculate Each Angle

Since \( m\angle PQR = 119^\circ \) and \( m\angle PQS = m\angle RQS \), we can find each angle by dividing \( 119^\circ \) by 2.
\[
m\angle PQS = m\angle RQS = \frac{119^\circ}{2} = 59.5^\circ
\]

Answer:

\( m\angle PQS = \boxed{59.5}^\circ \)
\( m\angle RQS = \boxed{59.5}^\circ \)