Question

In cyclic quadrilateral ABCD, ∠A = 3∠C and ∠D = 5∠B. Find the measure of each angle of the quadrilateral.

Answer 1

ABCD is a cyclic quadrilateral.

∴ ∠A + ∠C = 180°

`=>` 3∠C + ∠C = 180°

`=>` 4∠C = 180°

`=>` ∠C = 45°

∵ ∠A = 3∠C

`=>` ∠A = 3 × 45°

`=>` ∠A = 135°

Similarly,

∴ ∠B + ∠D = 180°

`=>` ∠B + 5∠B = 180°

`=>` 6∠B = 180°

`=>` ∠B = 30°

∵ ∠D = 5∠B

`=>` ∠D = 5 × 30°

`=>` ∠D = 150°

Hence, ∠A = 135°, ∠B = 30°, ∠C = 45°, ∠D = 150°