Question

In the figure 6.116. if lines PQ and RS intersect at a point T such that angle prt equal 40°, RPT equal 95°and tsq equal 75°find angle SQT​

Answer 1

Answer:

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.

Answer 2

IN TRIANGLE PRT ..........

angle p + angle r + angle t = 180°

95° + 40° + angle t = 180°

angle t = 180 - 135

angle t = 45 °

IN TRIANGLE STQ .........

angle t + angle s + angle q = 180°

45° + 75 ° + angle q = 180°

angle q = 180-120

angle q = 60°

angle sqt = 60°