Question

PQRS is a cyclic quadrilateral. If $\angle Q=\angle R={65}^{\circ },$ then find $\angle P$= ___ and $\angle S$ = __.

Answer 1

Consider the cyclic quadrilateral PQRS. Since opposite angles are supplementary,
$\angle P+\angle R={180}^{\circ }.$
$\therefore \angle P={180}^{\circ }–\angle R={180}^{\circ }–{65}^{\circ }={115}^{\circ }$
Similarly,
$\angle Q+\angle S={180}^{\circ }.$
$\therefore \angle S={180}^{\circ }–\angle Q={180}^{\circ }–{65}^{\circ }={115}^{\circ }.$