Math  /  Geometry

Questionnthe given figure, RLundefinedQPundefined\overrightarrow{R L} \| \overrightarrow{Q P}. Find PRS\angle P R S if mPQR=46m \angle P Q R=46^{\circ} and mQPR=65m \angle Q P R=65^{\circ}.

Studdy Solution
Since RLundefinedQPundefined\overrightarrow{RL} \| \overrightarrow{QP}, by the Alternate Interior Angles Theorem, we know that QRP=PRS\angle QRP = \angle PRS.
Therefore, mPRS=mQRP=69 m \angle PRS = m \angle QRP = 69^\circ .
The measure of PRS\angle PRS is:
69 \boxed{69^\circ}

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