Question

the angles of a quadrilateral are in ratio 3:5:7:9.Find the measures of each of these angles

Answer 1

Let ABCD is the quadrilateral.

Let ∠A = 3x, ∠B = 5x, ∠C = 7x, ∠D = 9x

now, ∠A + ∠B + ∠C + ∠D = 360⁰ [Angle sum property of quadrilateral]

3x + 5x + 7x + 9x = 360⁰

⇒ 24x = 360⁰ ⇒ x = 15

so, ∠A = 3 × 15 = 45⁰

∠B = 5 × 15 = 75⁰

∠C = 7 × 15 = 105⁰

∠D = 9 × 15 = 135⁰