Question

In the given figure, line RT is drawn parallel to SQ. If $\angle QPS={100}^{\circ }$, $\angle PQS={40}^{\circ }$, $\angle PSR={85}^{\circ }$ and $\angle QRS={70}^{\circ }$, then $\angle QRT=\_\_\_\_\_\_\_$.

• A. ${45}^{\circ }$
• B. ${65}^{\circ }$
• C. ${85}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (B)

${65}^{\circ }$

From the figure

In $△PQS,$

$\angle PQS+\angle QPS+\angle PSQ={180}^{\circ }$

$⟹\angle PSQ={180}^{\circ }-\angle QPS-\angle PQS={180}^{\circ }-{100}^{\circ }-{40}^{\circ }={40}^{\circ }$

Given $\angle PSR={85}^{\circ }⟹\angle PSQ+\angle QSR={85}^{\circ }⟹\angle QSR={85}^{\circ }-\angle PSQ={85}^{\circ }-{40}^{\circ }={45}^{\circ }$

In $△QSR$

$\angle QRS+\angle PSQ+\angle SQR={180}^{\circ }$

$\angle SQR={180}^{\circ }-\angle QRS-\angle QSR={180}^{\circ }-{70}^{\circ }-{45}^{\circ }={65}^{\circ }$

AS $RT\parallel SQ$

$\angle QRT=\angle SQR={65}^{\circ }$ $(\because alternativeangles)$