Question

in a cyclic quadrilateral abcd twice the measure of angle A is thrice the measure of angle C. find the measure of angle C​

Answer 1

Answer:

90 degree

Step-by-step explanation:

in a cyclic quadilateral,

opposite angles add upto 180 degree.

= angle A + angle C = 180 degree

now, let angle A be 2x

angle C = 3y

= 2x + 3y = 180

= 2(3y) = 180

= 6y = 180

= y = 30

= angle C = 3*30 = 90 degree

Answer 2

Answer:

The answer is 72°

Step-by-step explanation:

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