Question
In the given figure, $\triangle\text{ABC}$ is an equilateral triangle. Find $\text{m}\angle\text{BEC}.$
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Answer
Since, $\triangle\text{ABC}$ is an equilateral triangle Then, $\angle\text{BAC}=60^\circ$$\therefore\angle\text{BAC}+\angle\text{BEC}=180^\circ$ [Opposite angle of cyclic quad.]
$\Rightarrow60^\circ+\angle\text{BEC}=180^\circ$
$\Rightarrow\angle\text{BEC}=180^\circ-60^\circ=120^\circ$
$\Rightarrow60^\circ+\angle\text{BEC}=180^\circ$
$\Rightarrow\angle\text{BEC}=180^\circ-60^\circ=120^\circ$
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