PQRS is a cyclic quadrilateral. If ∠ P is four times ∠ R and ∠ S is three times ∠ Q, then sum of the measures of ∠ S and ∠ R will be:

PQRS is a cyclic quadrilateral. If ∠ P is four times ∠ R…

PQRS is a cyclic quadrilateral. If $\angle$ P is four times $\angle$ R and $\angle$ S is three times $\angle$ Q, then sum of the measures of $\angle$ S and $\angle$ R will be:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 171º

Given that

In cyclic quadrilateral

$\angle$ P + $\angle$ R = 180º

4x + x = 180º

5x = 180º

x = 36º

And

$\angle$ S + $\angle$ Q = 180º

3y + y = 180º

4y = 180º ⇒ y = 45º

Sum of $\angle$ S and $\angle$ R = 3y + x = 3 * 45º + 36º

= 135 + 36 = 171º

SSC CHSL 2021 PYQ — Question 51