Question

In a cyclic quadrilateral ABCD, twice the mearure of angle A is thrice the measure of angle C. find the measure of angle C. ​

Answer 1

Twice the measure of angle A is thrice the measure of angle C:

⇒ 2A = 3C

⇒ A : C = 3 : 2

Define x:

Let x be the constant ratio

A : C = 3x : 2x

Cyclic quadrilateral is a quadrilateral inscribed in a circle.

⇒ The sum of the opposite angles of a cyclic quadrilateral is supplementary.

Solve x:

3x + 2x = 180

5x = 180

x = 36º

Find Angle C:

Angle C = 2x = 2(36) = 72º

Answer: Angle C is 72º

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