In the given figure, ∆ABC is equilateral.

Question:

In the given figure, ABC is equilateral. Find

(i) ∠BDC,

(ii) ∠BEC.

Solution:

(i)
Given: ΔABC is an equilateral triangle.
i.e., each of its angle = 60°
⇒ BAC = ABC = ACB = 60°
Angles in the same segment of a circle are equal.
i.e., BDC = BAC = 60°
∴ BDC = 60°
(ii)
The opposite angles of a cyclic quadrilateral are supplementary.
Then in cyclic quadrilateral ABEC, we have:
BAC + BEC = 180°
⇒ 60° + BEC = 180°
⇒ BEC = (180° – 60°) = 120°
∴ BDC = 60° and BEC = 120°

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