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In a cyclic quadrilateral $ABCD$ , twice the measure of $∠ A$ is thrice the measure of $∠ C$ . Then, which of the following is the measure of $∠ C$ ?

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36 °

72 °

90 °

108 °

answer is B.

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Detailed Solution

Given that,

ABCD

is a cyclic quadrilateral.
Also,

2 ∠ A = 3 ∠ C

∠ A = \frac{3}{2} ∠ C . . . . . . . (1)

We know that,
Sum of opposite angles of cyclic quadrilateral are supplementary.
Then,

∠ A + ∠ C = 180^{o}

\Rightarrow \frac{3}{2} ∠ C + ∠ C = 180^{o}

[From

(1)

]

\Rightarrow \frac{5}{2} ∠ C = 180^{o}

\Rightarrow ∠ C = \frac{2 \times 180^{o}}{5} = 72^{o}

Hence, the measure of

∠ C

72^{o}

.
Therefore, option 2 is correct.

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