Question

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

• A. $36$
• B. $72$
• C. $90$
• D. $108$

Answer 1

Answer: (B)

$72$

In a cyclic quadrilateral, opposite angles are supplementary.

$\Rightarrow \angle A+\angle C={180}^0$

Gien that

$\Rightarrow 2\angle A=3\angle C$

$\Rightarrow \angle A=1.5\angle C$

$\Rightarrow 1.5\angle C+\angle C={180}^0$

$\Rightarrow 2.5\angle C={180}^0$

$\Rightarrow \angle C={72}^0$