Question

PQRS is a parallelogram and PA, SB, RC, QD, are angle bisectors. If PQ = QD = 6 units, find $\angle PQR.$

• A. 30${}^{\circ }$
• B. 60${}^{\circ }$
• C. 120${}^{\circ }$
• D. Indeterminate

Answer 1

The correct option is C 120${}^{\circ }$

Given : $P,Q,R,S$ is parallelogram.

$PQ=QD=6\text{unit}$

$\because PQ=QD$

$\therefore \angle OPD=\angle PDO$

$\therefore \angle PQD=180°-4x$

$\therefore \angle PQR=2(180°-4x)$

$\angle PQR=360°-8x$

$\therefore \angle PQR+\angle QPS=180°$

$360°-8x+2x=180°$

$-6x=-180°$

$x=30°$

$\therefore PQR=360°-(8\times 30)$

$=360°-240°$

$=120°$