Question : S and T are points on the sides PQ and PR, respectively, of $\triangle$PQR such that PS × PR = PQ × PT. If $\angle$Q = 96° and $\angle$PST = $\angle$PRQ + 34°, then $\angle$QPR = ?
Option 1: 24°
Option 2: 25°
Option 3: 22°
Option 4: 26°
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
Correct Answer: 22°
Solution :
According to the question,
PS × PR = PQ × PT
⇒ $\frac{PQ}{PS}$ = $\frac{PR}{PT}$
⇒ ST || QR
$\angle$ Q = $\angle$ PST = 96° (corresponding angles between two parallel lines)
Since $\angle$ PST = $\angle$ PRQ + 34°
⇒ 96° = $\angle$ PRQ + 34°
⇒ $\angle$ PRQ = (96° – 34°) = 62°
Now,
⇒ $\angle$ PQR + $\angle$ PRQ + $\angle$ QPR = 180°
⇒ 96° + 62° + $\angle$QPR = 180°
⇒ 158° + $\angle$QPR = 180°
⇒ $\angle$QPR = 180° – 158°
⇒ $\angle$QPR = 22°
Hence, the correct answer is 22°.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
