question_answer

In a \[\Delta PQS,\]R is a point on PS such that PR = QR and QS = RS. If \[\angle RSQ=120{}^\circ ,\] what is the measure of \[\angle QPR\]?

A)  \[30{}^\circ \]

B)  \[15{}^\circ \]

C)  \[45{}^\circ \]

D)  \[60{}^\circ \]

Correct Answer: B

Solution :

\[\because RS=SQ\] \[\therefore \]      \[\angle QRS=\frac{1}{2}(180{}^\circ -120{}^\circ )=30{}^\circ \] Hence, \[\angle QRS=\frac{1}{2}(180{}^\circ -150{}^\circ )=15{}^\circ \]\[(\because PR=RQ)\]