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°.