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 = ?

22° 24° 30° 62°

24°

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°