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

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#### 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
∠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°

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#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(A) | Q: 55 | Page no. 262

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