Question

In the figure given above, $PQ$ is parallel to $RS$. What is $\angle NMS$ equal to?

• A. ${20}^{\circ }$
• B. ${23}^{\circ }$
• C. ${27}^{\circ }$
• D. ${47}^{\circ }$

Answer 1

The correct option is A ${20}^{\circ }$

Draw $l\parallel PQ$ through $N$
$\angle LNX=\angle NLQ$ .....(alternate angles)
$\therefore \angle LNX={47}^{\circ }$
$\angle XNM={67}^{\circ }-{47}^{\circ }={20}^{\circ }$
$\angle NMS=\angle XNM$ (alternate angles)
$\therefore \angle NMS={20}^{\circ }$