S and T are points on the sides PQ and PR, respectively of ΔPQR such that PS × PR = PQ × PT. If ∠Q = 94° and ∠PST + ∠PRQ = 32°, then ∠QPR = ?
Answer & explanation
Correct answer: option 2
In ΔPQR
PS ×PR = PQ × PT
\(\frac{PQ}{PR}\) = \(\frac{PS}{PT}\)
as ST || QR ⇒ ∠PST = ∠PQR
Let ∠PRQ = x° ∴ ∠PST = x + 32°
⇒ x + 32° = 94°
⇒ x = 62°
∠QPR = 180° - 62° - 94° = 24°