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

Given, ∠PRT = 40°, ∠RPT = 95°, ∠TSQ = 75°
According to the question,
∠PRT + ∠RPT + ∠PTR = 180° (Sum of the interior angles of the triangle)
⇒ 40° + 95° + ∠PTR = 180°
⇒ 135° + ∠PTR = 180°
⇒ ∠PTR = 45°
∠PTR = ∠STQ = 45° (Vertically opposite angles)
Now, ∠TSQ + ∠PTR + ∠SQT = 180° (Sum of the interior angles of the triangle)
75° + 45° + ∠SQT = 180°
⇒ 120° + ∠SQT = 180°
⇒ ∠SQT = 60°