Question

In figure, $PARS$ is cyclic quadrilateral whose diagonal intersect at $A$ if $\angle SQR={80}^0$ and $\angle QPR={30}^0$, then find $\angle SRQ$.

Answer 1

Given : $\angle SQR={80}^0$
Now $\angle SQR=\angle SPR$ [angles of same segment]
$\therefore \angle SPR={80}^0$
$\therefore \angle SPQ=\angle SPR+\angle RPQ$
$={80}^0+{30}^0$
or $\angle SPQ={110}^0$
but $\angle SPQ+\angle SRQ={180}^0$ [Sum of opposite angles of cyclic quadrilateral]
$\therefore \angle SRQ={180}^0–\angle SPQ$
$={180}^0–{110}^0={70}^0$
Thus, $\angle SRQ={70}^0$