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प्रश्न
In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?
विकल्प
36°
72°
90°
108°
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उत्तर
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)]
⇒ `(3/2 + 1) ∠C = 180^circ`
⇒ `5/2 ∠C = 180^circ`
⇒ `∠C = (2 xx 180^circ)/5`
⇒ ∠C = 72º
Thus, the measure of ∠C is 72º.
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