Question 12 Marks
In the given figure, $\triangle\text{ABC}$ is an equilateral triangle. Find $\text{m}\angle\text{BEC}.$
Answer
View full question & 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.]
$\Rightarrow60^\circ+\angle\text{BEC}=180^\circ$
$\Rightarrow\angle\text{BEC}=180^\circ-60^\circ=120^\circ$
Then, $\angle\text{BAC}=60^\circ$
$\therefore\angle\text{BAC}+\angle\text{BEC}=180^\circ$ [Opposite angle of cyclic quad.]
$\Rightarrow60^\circ+\angle\text{BEC}=180^\circ$
$\Rightarrow\angle\text{BEC}=180^\circ-60^\circ=120^\circ$
