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

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KollegeApply · Accepted Answer

72º Explanation: ABCD is a cyclic quadrilateral. 2$\angle$A = 3$\angle$C ...(1) (Given) Now, $\angle$A + $\angle$C = 180º ...(Opposite angles of a cyclic quadrilateral are supplementary) $\Rightarrow$ $\frac{3}{2}$ $\angle$C + $\angle$C = 180^circ ...[From (1)] ​$\Rightarrow$ ($\frac{3}{2}$ + 1) $\angle$C = 180^circ ​$\Rightarrow$ $\frac{5}{2}$ $\angle$C = 180^circ $\Rightarrow$ $\angle$C = (2 xx 180^circ)/5 $\Rightarrow$ $\angle$C = 72º Thus, the measure of $\angle$C is 72º.

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