$A B C$ is an equilateral triangle. Find $∠ B E C$ .

30^{\circ}

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60^{\circ}

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90^{\circ}

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120^{\circ}

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Solution

The correct option is D $120^{\circ}$
$I n △ A B C i s e q u i l a t e r a l T r i a n g l e \Rightarrow ∠ A = ∠ B = ∠ C = 60 (A n g l e s o f e q u i a l a t e r a l t r i a n g l e a r e e q u a l t o 60 S i n c e A B C D i s a c y c l i c q u a d i l a t e r a l ∠ B A C + ∠ B E C = 180 (O p p o s i t e a n g l e s o f c y c l i c q u a d i l a t e r a l a r e s u p p l e m e n t a r y) ∠ B A C = 60 \Rightarrow ∠ B E C = 180 - 60 = 120 H e n c e o p t i o n (D) i s r i g h t a n s w e r$

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