S and T are points on the sides PQ and PR, respectively of △PQR such that PS × PR = PQ × PT. If ∠Q = 96º and ∠PST = ∠PRQ + 34º, then ∠QPR = ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 22º
PS × PR = PQ × PT
⇒ PS/PQ = PT/PR
So one can say that,
△PQR is similar to the △PST.
So ST || QR , ∠PST = 96°
It is given that,
∠PST = ∠PRQ + 34º
∠PRQ = 96 - 34 = 62°
By using triangle angle sum property,
∠QPR = 180 - ∠PQR - ∠PRQ
∠QPR = 180 - 96 - 62 = 22°