Question

In the given figure, $△$ABC is equilateral. Find $\left(i\right)\angle BDC,\left(ii\right)\angle BEC.$

Answer 1

ANSWER:
(i)
Given: Δ ABC 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°