Question

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

Answer 1

In the given figure, lines PQ and RS intersect at point T, such that 

∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°. In ∆PRT 

∠PRT + ∠RPT + ∠PTR = 180° 

[Angle sum property of a triangle] 

⇒ 40° + 95° + ∠PTR = 180° 

⇒ 135° + ∠PTR = 180° 

⇒ ∠PTR = 180° – 135° = 45° 

Also, ∠PTR = ∠STQ 

[Vertical opposite angles] 

∴ ∠STQ = 45°

Now, in ∆STQ, 

∠STQ + ∠TSQ + ∠SQT = 180° [Angle sum property of a triangle] 

⇒ 45° + 75° + ∠SQT = 180° 

⇒ 120° + ∠SQT = 180° 

⇒ ∠SQT = 180° – 120° = 60° 

Hence, ∠SQT = 60° Ans.