Mathematics
In the given figure, O is the centre of the circle and ΔABC is equilateral. Find :
(i) ∠BDC
(ii) ∠BEC.
Answer
(i) Since ABC is an equilateral triangle so,
∠A = ∠B = ∠C = 60°.
From figure,
∠BDC = ∠BAC (Angles in same segment are equal.)
∴ ∠BDC = 60°.
Hence, ∠BDC = 60°.
(ii) BDCE is a cyclic quadrilateral. Hence, sum of the opposite angles = 180°.
⇒ ∠BDC + ∠BEC = 180°
⇒ 60° + ∠BEC = 180°
⇒ ∠BEC = 180° - 60° = 120°.
Hence, ∠BEC = 120°.
Related Questions
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