The area of APRS is half the area of APQS which means that PR is a median. So QR = RS Also QR = PR (∴∆PQR is an equilateral triangle) Hence, PR = RS Now ∠PRQ = 60° ⇒ ∠PRS = 120° So, ∠RPS + ∠PSR = 60° But ∠RPS = ∠PSR (∴ PR = RS) =∠RPS =30° Therefore, ZQPS = 60° + 30° = 90°