Mathematics
In the figure (i) given below, triangle ABC is equilateral. Find ∠BDC and ∠BEC.
Circles
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Answer
Since ABC is an equilateral triangle so,
∠A = ∠B = ∠C = 60°.
From figure,
∠BDC = ∠BAC (∵ angles in alternate segments are equal.)
∴ ∠BDC = 60°.
BDCE is a cyclic quadrilateral. Hence, sum of the opposite angles = 180°.
⇒ ∠BDC + ∠BEC = 180°
⇒ 60° + ∠BEC = 180°
⇒ ∠BEC = 180° - 60° = 120°.
Hence, the value of ∠BDC = 60° and ∠BEC = 120°.
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