Question

In the given figure, $PQRS$ is an isosceles trapezium and $\overline{PQ}||\overline{SR}||\overline{MN}$. If $\angle SPM=70^{\circ }$ and $\angle PQR=110^{\circ }$, then find $\angle PMN$.

• A. $140^{\circ }$
• B. $150^{\circ }$
• C. $120^{\circ }$
• D. $100^{\circ }$

Answer 1

Answer: (A)

Given that $PQRS$ is an isosceles trapezium, $\overline{PQ}||\overline{SR}||\overline{MN}$.
$\angle SPM=70^{\circ }$ and $\angle PQR=110^{\circ }$ (given)
$\Rightarrow \angle PQR=\angle SPQ=110^{\circ }$
$\angle MPQ=\angle SPQ-\angle SPM=110^{\circ }-70^{\circ }$ $=40^{\circ }$
$\overline{PQ}||\overline{MN}\Rightarrow \angle PMN=180^{\circ }-\angle MPQ$
$=180^{\circ }-40^{\circ }=140^{\circ }$