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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?

Options

  • 36

  • 72

  • 90

  • 108

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Solution 1

ABCD is a cyclic quadrilateral.

2∠A = 3∠C        .....(1) (Given)

Now,

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

quadrilateral are supplementary)

⇒ \[\frac{3}{2}\] ∠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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