A) \[30{}^\circ \]
B) \[40{}^\circ \]
C) \[60{}^\circ \]
D) \[80{}^\circ \]
Correct Answer: C
Solution :
\[m\,\,\angle TRQ=m\,\,\angle RST\] [Angles in alternate segment] But \[m\,\,\angle TRQ=30{}^\circ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow m\,\,\angle RST=30{}^\circ \] Also, \[m\,\,\angle SRT=90{}^\circ \] \[\therefore \,\]\[m\,\,\angle RTS=180{}^\circ -(90{}^\circ +30{}^\circ )=60{}^\circ \] \[\Rightarrow \]\[m\,\angle PRS=m\,\,\angle RTS\,\,\,\,\,\,\,\,\,\Rightarrow \angle PRS=60{}^\circ \]You need to login to perform this action.
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