In the given figure, $△ A B C$ is an equilateral triangle. What is the value of $∠ B E C$ ?

80^{\circ}

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100^{\circ}

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120^{\circ}

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130^{\circ}

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Solution

The correct option is C $120^{\circ}$
Here, $A B E C$ is a cyclic quadrilateral.
We know, sum of its opposite angles are equal to $180^{o}$ .

$\Rightarrow ∠ B A C + ∠ B E C = 180^{\circ}$

$\Rightarrow 60^{o} + ∠ B E C = 180^{\circ}$

$\Rightarrow ∠ B E C = 180^{\circ} - 60^{\circ} = 120^{\circ}$ .

Hence, option $C$ is correct.

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In the given figure, △ABC is an equilateral triangle. What is the value of ∠BEC?

The correct option is C 120∘Here, ABEC is a cyclic quadrilateral.We know, sum of its opposite angles are equal to 180o.⇒∠BAC+∠BEC=180∘⇒60o+∠BEC=180∘⇒∠BEC=180∘−60∘=120∘.Hence, option C is correct.

In the given figure, $△ A B C$ is an equilateral triangle. What is the value of $∠ B E C$ ?