SSC CHSL 15 Oct 2020 Shift 1 Paper

© examsiri.com

Question : 58 of 100

Marks: +1, -0

In

\Δ\PQR

, the side QR is extended to S such that,

\RS=\PR

. If

\∠\QPS=110°

and

\∠\PRQ=70°

, then the value of

\∠\PQR

is

$50°$
$40°$
$35°$
$45°$

Solution:

Let

\∠\PSR

be

x °

.
From the figure,

\∠\PRQ+\∠\PRS=180°

⇒

70°+\∠\PRS=180°

⇒

\∠\PRS=110°

\ln \Δ\PRS

,

\RS=\PR

Angles opposite to equal sides are equal.
∴

\∠\RPS=\∠\PSR=x°

∴

\∠\PRS+\∠\RPS+\∠\PSR=180°

⇒

110°+x+x=180°

⇒

2 x=180°-110°=70°

⇒ x = 35°
Now,

\∠\QPR+\∠\RPS=110°

[\∵∠\QPS=110°]

∴

\∠\QPR=110°-35°=75°

In

\Δ\PQR

,

\∠\PQR+\∠\PRQ+\∠\QPR=180°

⇒

\∠\PQR+70°+75°=180°

⇒

\∠\PQR=180°-145°=35°

© examsiri.com

Go to Question:

Prev Question

Next Question