Question

4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that Z PRT=40°, ZRPT=95°
Fig. 6.39
Fig. 6.40
and ZTSQ = 75°, find Z SQT.​

Answer 1

In PRT

By angle sum property of triangle

∠PRT+∠RPT+∠PTR=180°

⇒90° +45°+∠PTR=180°

⇒135 °+∠PTR=180°

⇒∠PTR=180°−135

⇒∠PTR=45°

Also,

∠STQ=∠PTR

∠STQ=45°

(vertically opposite angles)

In ΔSQT

By angle sum property of triangle

∠SQT+∠STQ+∠TSQ=180°

∠SQT+75°+45°=180°

∠SQT+120° =180°

∠SQT=180°−120°

∠SQT=60°