Question

In the figure, $\Delta ABC$ is an equilateral triangle. Find m$\angle BEC$.

Answer 1

$\because \Delta ABC$ is an equilateral triangle .

$\therefore \angle A={60}^{\circ }$

$\because ABEC$ is a cyclic quadrilateral.

$\therefore \angle A+\angle E={180}^{\circ }$ (Sum of opposite angles)

$\Rightarrow {60}^{\circ }+\angle E={180}^{\circ }$

$\Rightarrow \angle E={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\therefore m\angle BEC={120}^{\circ }$