Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

In $△$PRT, $\angle$P + $\angle$R + $\angle$1 = ${180}^{\circ }$ (angle sum property)

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

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

$\angle$1 = $\angle$2 (vertically opposite angles)

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

In $△$TQS, $\angle$2 + $\angle$Q + ${75}^{\circ }$ = ${180}^{\circ }$

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

$\angle$Q + ${120}^{\circ }$ = ${180}^{\circ }$

$\angle$Q = ${180}^{\circ }$ – ${120}^{\circ }$

$\angle$Q = ${60}^{\circ }$

$\angle$SQT = ${60}^{\circ }$
2 ($\angle$SQT) = ${120}^{\circ }$