Question

PQRS is a cyclic quadrilateral. Given $\angle$QPS $={73}^o$, $\angle$PQS$={55}^o$ and $\angle$PSR$={82}^o$, calculate $\angle$QRS.

Answer 1

In a cyclic quadrilateral, the sum of opposite angles is 180 degrees, so

$\angle QRS+\angle QPS={180}^o\Rightarrow \angle QRS={180}^o-{73}^o={107}^o$