Question

$PQRS$ is cyclic quadrilateral such that $PR$ is the diameter of the circle.

If $\angle QPR={50}^{\circ },\angle SPR={66}^{\circ },$ then $\angle QRS$ is:

• A. ${50}^{\circ }$
• B. ${64}^{\circ }$
• C. ${110}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is B ${64}^{\circ }$

REF.Image

PQRS is cyclic quadrilateral

$\to$ Opposite angles of cycilc quadrilateral are supplementary.

$\therefore \angle QPS+\angle QRS={180}^{\circ }$

$\angle QRS=180-\angle QPS$

$={180}^{\circ }-\angle QPR-\angle SPR$

$=180-50-66$

$={64}^{\circ }$