Question

The diagonals of a parallelogram PQRS intersect at O. If $\angle QOR={90}^{\circ }and\angle QSR={50}^{\circ },then\angle ORS$ is :

• A. ${90}^{\circ }$
• B. ${40}^{\circ }$
• C. ${70}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

Given: $\angle QOR={90}^{\circ }and\angle QSR={50}^{\circ }$

Now, $\angle SOR={180}^{\circ }-\angle QOR={90}^{\circ }$ (Since angles forming a linear pair are complementary)

Consider $\Delta SOR$,

$\angle SOR+\angle OSR+\angle ORS={180}^{\circ }$ (angle sum property of triangles)

$\therefore \angle ORS={180}^{\circ }-{90}^{\circ }-{50}^{\circ }={40}^{\circ }$