PQRS is a cyclic quadrilateral and PQ is a diameter of the circle. If ∠RPQ = 23°, then what is the measure of ∠PSR?

113°

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 = \({113}^\circ\)