SSC CHSL 16 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

© examsiri.com

Question : 70 of 100

Marks: +1, -0

P Q R S

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

$192^{∘}$
$175^{∘}$
$171^{∘}$
$165^{∘}$

Solution:

Let

∠ R=x^{∘}

then

∠ P=4 x^{∘}

and

∠ Q=y^{∘}

then

∠ S=3 y^{∘}

Since,

P Q R S

is cyclic quadrilateral.

∴ x+4 x=180^{∘} ⇒ 5 x=180

⇒ \;\; x=\;{180^{∘}}/{5}=36^{∘}

and

\;\; y+3 y=180^{∘}

⇒ \;\; 4 y=180^{∘}

⇒ \;\; y=\;{180^{∘}}/{4}

⇒ \;\; y=45^{∘}

∴ ∠ S+∠ R=3 y+x

=3 × 45^{∘}+36^{∘}

=135^{∘}+36^{∘}=171^{∘}

© examsiri.com

Go to Question:

Prev Question

Next Question