Question

In quadrilateral PQRS, if ∠P = 60° and ∠Q : ∠R : ∠S = 2:5:8, then find the measure of∠R. * 4 points 40 degree 100 degree 120 degree 160 degree​

Answer 1

Answer:

Answers is 175°

Step-by-step explanation:

∠P = 60°

∠Q ∶ ∠R ∶ ∠S = 2 ∶ 3 ∶ 7

Concept

Angle sum property of quadrilateral : Sum of angles of a quadrilateral is 360°

Calculation

In quadrilateral PQRS, By angle sum property

∠P + ∠Q + ∠R + ∠S = 360°

⇒ ∠Q + ∠R + ∠S = 360° - 60° = 300°

∠Q ∶ ∠R ∶ ∠S = 2 ∶ 3 ∶ 7

⇒ ∠Q = 2x, ∠R = 3x and ∠S = 7x, where x is a positive integer

⇒ 2x + 3x + 7x = 300°

⇒ 12x = 300°

⇒ x = 25°

∴ ∠S = 7x = 7 × 25° = 175