#### Question

In a cyclic quadrilateral ABCD, ∠A : ∠C = 3 : 1 and ∠B : ∠D = 1: 5; Find each angle of the quadrilateral .

#### Solution

Let ∠A and ∠C be 3x and x respectively

In cyclic quadrilateral ABCD,

∠A + ∠C = 180°

(pairs of opposite angles in a cyclic quadrilateral are supplementary)

⇒ 3x + x = 180°

⇒ `x = (180°)/4 = 45°`

∴ ∠A = 135° and ∠C = 45°

Let the measure of ∠B and ∠D be y and 5y respectively In cyclic quadrilateral ABCD,

∠B + ∠D = 180°

(pair of opposite angles in a cyclic quadrilateral are supplementary are supplementary)

⇒ y +5y = 180°

⇒ `y =(180°)/6 =30°`

∴ ∠B= 30° and ∠D = 150°

Is there an error in this question or solution?

Solution In a Cyclic Quadrilateral Abcd, ∠A : ∠C = 3 : 1 and ∠B : ∠D = 1: 5; Find Each Angle of the Quadrilateral . Concept: Cyclic Properties.