Question

The diagonals PR and QS of a cyclic quadrilateral PQRS intersect at X. The tangent at P is parallel to QS. Prove that $PQ=PS$.

If m$\angle PQS={50}^o$, then m($\angle PRS$) is

Answer 1

Chords $PS$ subtends.
$\angle PQS$ and $\angle PRS$ in the same segment.
$\angle PQS=\angle PRS$
$\angle PQS=80°$ [L subtended by same chord / arc in same segment in equal]
$\angle PQR=80+50=130\angle PQR+\angle PSR=180$(sum of opposite angle of cyclic quadrilaterals is 180°)
$130+\angle PSR=180\angle PSR=50°$
And as we know $\angle PQS=50\therefore \angle PRS=360-(\angle PQS+\angle PSR)=360-100=260$