In figure AOB is a diameter if the circle and C, D and E are any three points of the semicircle. Find the value of ∠ACD + ∠BED.

ACDE is a cyclic quadrilateral because A, C, D and E are four points on circle.

Construction: Join AE

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

⇒∠ACD + ∠AED = 180° … (1)

Given AOB is a diameter.

We know that diameter subtends a right angle to the circle.

⇒∠AEB = 90°

On adding equations (1) and (2),

⇒∠ACD + ∠AED + ∠AEB = 180° + 90° = 270°

∴ ∠ACD + ∠BED = 270°