PQRS is a cyclic quadrilateral and PQ is a diameter of the circle. If ∠RPQ = 23°, then what is the measure of ∠PSR?
Answer & explanation
Correct answer: option 1
According to the concept, \(\angle\)PRQ = \({90}^\circ\)
Considering \(\Delta \)PRQ,
\(\angle\)RPQ + \(\angle\)RQP + \(\angle\)PRQ = \({180}^\circ\)
\({23}^\circ\) + \(\angle\)RQP + \({90}^\circ\) = \({180}^\circ\)
\(\angle\)RQP = \({180}^\circ\) - \({113}^\circ\)
\(\angle\)RQP = \({67}^\circ\)
Since the circle is circumscribed on a quadrilateral PQRS,
PQRS is a cyclic quadrilateral.
So, \(\angle\)RQP + \(\angle\)PSR = \({180}^\circ\)
\({67}^\circ\) + \(\angle\)PSR = \({180}^\circ\)
\(\angle\)PSR = \({180}^\circ\) - \({67}^\circ\)
\(\angle\)PSR = \({113}^\circ\)