Question

In the given figure, AOB is a diameter of the circle and C, D , E are any three points to semi circle then ∠ACD + ∠BED = _______

Answer 1

Given:
AOB is a diameter of the circle


We know, the diameter subtends a right angle to any point on the circle.
∴ ∠AEB = 90° ...(1)


Quadrilateral ACDE is a cyclic quadrilateral.

In a cyclic quadrilateral, the sum of opposite angles is 180^∘.
Thus, ∠ACD + ∠DEA = 180° ...(2)


Adding (1) and (2), we get
∠ACD + ∠DEA + ∠AEB = 90° + 180°
⇒ ​∠ACD + ∠DEB = 270°


Hence, ∠ACD + ∠BED = 270°.