Question

In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?

Options

• 36°

• 72°

• 90°

• 108°

Answer 1

72º

Explanation:

ABCD is a cyclic quadrilateral.

2∠A = 3∠C   ...(1) (Given)

Now, ∠A + ∠C = 180º   ...(Opposite angles of a cyclic quadrilateral are supplementary)

⇒ `3/2 ∠C + ∠C = 180^circ`   ...[From (1)]

​⇒ `5/2 ∠C = 180^circ`

⇒ `∠C = (2 xx 180^circ)/5`

⇒ ∠C = 72º

Thus, the measure of ∠C is 72º.