Question

29. In the figure if lines PQ and RS. Intersect at point T Such that PRT = 40°, RPT = 95°
and TRQ = 75°. Find SQT.​

Answer 1

To Find:-

• The ∠SQT

Given:-

• ∠PRT = 40°
• ∠RPT = 95°
• ∠TRQ = 75°

Solution:-

In ∆PRT

∠PRT + ∠RPT + ∠PTR = 180°

( by angle sum property of triangle )

A . T . Q

⟹ 45° + 95° + ∠PTR = 180°

⟹ 135° + ∠PTR = 180°

⟹ ∠PTR = 180° - 135°

⟹ ∠PTR = 45°

Now, Finally

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

In ∆SRT

∠SQT + ∠STQ + ∠TSQ = 180°

( by angle sum property of triangle )

⟹ ∠SQT + 75° + 45° = 180°

⟹ ∠SQT + 120° = 180°

⟹ ∠SQT = 180° - 120°

⟹ ∠SQT = 60°