Question

In a cyclic quadrilateral ABCD, If $m\angle A=3\left(m\angle C\right)$. Find $m\angle A$.

Answer 1

In cyclic quadrilateral ABCD, $m\angle A=3\left(m\angle C\right)$.

$\because$ ABCD is a cyclic quadrilateral,

$\therefore \angle A+\angle C={180}^{\circ }$

$\Rightarrow 3\angle C+\angle C={180}^{\circ }\Rightarrow 4\angle C={180}^{\circ }$

$\Rightarrow \angle C=\frac{{180}^{\circ }}{4}={45}^{\circ }$

$\therefore \angle A=3\times {45}^{\circ }={135}^{\circ }$

Hence, $m\angle A={135}^{\circ }$