4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°, find ∠SQT.
Solution: Consider triangle PRT. ∠PRT +∠RPT + ∠PTR = 180° So, ∠PTR = 45° Now ∠PTR will be equal to ∠STQ as they are vertically opposite angles. So, ∠PTR = ∠STQ = 45° Again, in triangle STQ, ∠TSQ +∠PTR + ∠SQT = 180° Solving this we get, 74° + 45° + ∠SQT = 180° ∠SQT = 60°
