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 = 180º     ...[From (1)]

​⇒ `5/2`∠C = 180º

⇒ ∠C = `(2 xx 180º)/5`

⇒ ∠C = 72º

Thus, the measure of ∠C is 72º.