question_answer

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

A)  \[30{}^\circ \]                         

B) \[15{}^\circ \]

C)  \[45{}^\circ \]                         

D)  \[60{}^\circ \]

Correct Answer: B

Solution :

PS = SQ

\[\angle QRS=\frac{1}{2}[180{}^\circ -120{}^\circ ]=30{}^\circ \]

\[\angle QRP=(180{}^\circ -30{}^\circ )=150{}^\circ \]

Hence, \[\angle QPR=\frac{1}{2}(180{}^\circ -150{}^\circ )=15{}^\circ \]

\[\because \](PR = RQ)