In Δ PQR, PQ = PR and S is a point on QR such that ∠ PSQ = 96º + ∠ QPS and ∠ QPR = 132º. What is the measure of ∠ PSR?

In Δ PQR, PQ = PR and S is a point on QR such that ∠ PSQ =…

In $\Delta$ PQR, PQ = PR and S is a point on QR such that $\angle$ PSQ = 96º + $\angle$ QPS and $\angle$ QPR = 132º. What is the measure of $\angle$ PSR?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 54º

$\angle$ QPR + $\angle$ PRQ + $\angle$ PQR = 180

132 + x + x = 180

2x = 48

x = 24°

$\angle$ PSQ + $\angle$ PQS + $\angle$ QPS = 180

96º + $\angle$ QPS + $\angle$ QPS + 24 = 180

$\angle$ QPS = 30°

$\angle$ QSP = 96 + 30 = 126°.

$\angle$ QSP + $\angle$ PSR = 180°( Linear pair)

$\angle$ PSR = 180 - 126 = 54°.

SSC CGL 2022 PYQ — Question 6