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In a Cyclic Quadrilateral Abcd, ∠A : ∠C = 3 : 1 and ∠B : ∠D = 1: 5; Find Each Angle of the Quadrilateral . - ICSE Class 10 - 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
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.
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