Question

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

Answer 1

PQ and RS stright lines intersect at T.

If ∠PRT = 40°, ∠RPT = 95°, and

∠TSQ = 75°, then ∠SQT = ?

In ∆PRT,

∠RPT + ∠PRT + ∠PTR = 180°

95 + 40 + ∠PTR = 180°

135 + ∠PTR = 180

∠PTR = 180 – 135

∴ ∠PTR = 45°

∠PTR = ∠STQ = 45°

(∵ Vertically opposite angles)

In ∆TSQ,

∠STQ + ∠TSQ + ∠SQT =180

45 + 75 + ∠SQT = 180

120 + ∠SQT = 180

∴∠SQT = 180 – 120

∴ ∠SQT = 60°.