Question

In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40, ∠RPT = 95 and ∠TSQ = 75, find ∠SQT.

Answer 1

Using angle sum property for ΔPRT, we obtain

∠PRT + ∠RPT + ∠PTR = 180

40 + 95 + ∠PTR = 180

∠PTR = 180 − 135

∠PTR = 45

∠STQ = ∠PTR = 45 (Vertically opposite angles)

∠STQ = 45

By using angle sum property for ΔSTQ, we obtain

∠STQ+ ∠SQT + ∠QST = 180

45 + ∠SQT + 75 = 180

∠SQT = 180 − 120

∠SQT = 60