Question

In the figure given below, if lines PQ and RS intersect at point T, such that,
$\angle PRT={40}^{\circ }$, $\angle RPT={95}^{\circ }$ and $\angle TSQ={75}^{\circ }$, then find $2\angle SQT$.

• A. ${120}^{\circ }$
• B. ${150}^{\circ }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$
• E. None of the above

Answer 1

The correct option is A

${120}^{\circ }$

$\text{In}△\text{PRT},\angle P+\angle R+\angle 1={180}^{\circ }$.
(Sum of all the interior angles of a triangle is ${180}^{\circ }$)

$\Rightarrow {95}^{\circ }+{40}^{\circ }+\angle 1={180}^{\circ }$

$\Rightarrow \angle 1={180}^{\circ }–{135}^{\circ }={45}^{\circ }$

$\Rightarrow \angle 1=\angle 2\text{(vertically opposite angles)}$

$\Rightarrow \angle 2={45}^{\circ }$

$\text{In}△\text{TQS},\angle 2+\angle SQT+\angle QST={180}^{\circ }$.
(Sum of all the interior angles of a triangle is ${180}^{\circ }$)

$\Rightarrow {45}^{\circ }+\angle SQT+{75}^{\circ }={180}^{\circ }$

$\Rightarrow \angle SQT+{120}^{\circ }={180}^{\circ }$

$\Rightarrow \angle SQT={60}^{\circ }$

$\Rightarrow 2\angle SQT={120}^{\circ }$