SSC CGL 2023 PYQ — Question 53

The correct answer is option 2 i.e. 74°.

Given that

In the given figure, $\Delta$QPS $\approx$ $\Delta$SRQ.

According to the question

⇒ 2x + 12 = 106

⇒ 2x = 106 - 12 = 94

⇒ x = 47

$\angle$SQR = $\angle$PSQ = 52° (opposite interior angle)

In triangle SQR, 

⇒ $\angle$SRQ + $\angle$QSR + $\angle$RQS = 180°

⇒ 2 × 47 + 12 + $\angle$QSR + 52° = 180°

⇒ 94 + 12 +  $\angle$QSR = 180° - 52° = 128°

⇒ $\angle$QSR = 128° - 106° = 22°

Hence, $\angle$PSR = $\angle$PSQ + $\angle$QSR = 52° + 22° = 74°