#### 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°

Is there an error in this question or solution?

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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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