Question : $\triangle PQR$ and $\triangle SQR$ are both isosceles triangles on a common base $QR$ such that $P$ and $S$ lie on the same side of $QR$. If $\angle QSR=60^{\circ}$ and $\angle QPR=100^{\circ}$, then find $\angle SRP$.
Option 1: $80^{\circ}$
Option 2: $60^{\circ}$
Option 3: $100^{\circ}$
Option 4: $20^{\circ}$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: $20^{\circ}$
Solution :
Given: That $\triangle PQR$ and $\triangle SQR$ are isosceles triangles, $\angle QPR =100^{\circ}$ and $\angle QSR = 60^{\circ}$.$\triangle PQR$ and $\triangle SQR$ are isosceles triangles, such that $PQ=PR$ and $QS=SR$.
$PQ=PR$
$\therefore \angle PQR=\angle PRQ$
$180^{\circ}=100^{\circ}+2 \angle PQR$
⇒ $\angle PQR=\angle PRQ=40^{\circ}$...(i)
⇒ $QS=RS$
$\therefore \angle QRS=\angle RQS$
⇒ $180^{\circ}=60^{\circ}+2 \angle QRS$
⇒ $\angle QRS=\angle SQR=60^{\circ}$...(ii)
$\therefore\angle SRP=\angle QRS-\angle QRP$
From equations (i) and (ii),
$\angle SRP=60^{\circ}-40^{\circ}=20^{\circ}$
Hence, the correct answer is $20^{\circ}$.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CHSL
