# Four alternative answers for the following question is given. Choose the correct alternative In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C? - Geometry

MCQ

Four alternative answers for the following question is given. Choose the correct alternative

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

• 36

• 72

• 90

• 108

#### Solution 1

ABCD is a cyclic quadrilateral.

2∠A = 3∠C        .....(1) (Given)

Now,

∠A + ∠C = 180º     ......(Opposite angles of a cyclic

⇒ $\frac{3}{2}$ ∠C + ∠C = 180º    [From (1)]

​⇒ $\frac{5}{2}$ ∠C = 180º

⇒ ∠C = $\frac{2 \times 180^\circ}{5}$ = 72º

Thus, the measure of ∠C is 72º.

Hence, the correct answer is 72º.

#### Solution 2

72

Concept: Property of Sum of Measures of Arcs
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