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

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Question

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

Solution

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°

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