Question

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BEC 

Answer 1

We know that the opposite angles of a cyclic quadrilateral are supplementary.

Thus, in cyclic quadrilateral BECD ,

∠ BEC + ∠ BDC = 180°

⇒ ∠ BEC + 32° = 180°

⇒ ∠ BEC = 180° - 32°

⇒ ∠ BEC = 148°