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In Fig. if ABC is an equilateral triangle. Find ∠BDC and ∠BEC

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Best answer

Since, 

ABC is an equilateral triangle 

Then, 

∠BAC = 60° 

Therefore, 

∠BDC = ∠BAC = 60° 

(Angles in the same segment) 

Since, 

quadrilateral ABEC is a cyclic quadrilateral 

Then, 

∠BAC + ∠BEC = 180° 

60° + ∠BEC= 180° 

∠BEC = 180° – 60° 

= 120°

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