In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ABC+∠CDE. Give reasons for your answer.
Join centre O and C and EC.
`∠AOC = (180°)/2 = 90°`
And ∠AOC = 2∠AEC
(Angle at the centre is double the angle at the circumference subtended by the same chord)
⇒`∠AEC = (90°)/2 = 45°`
Now, ABCE is a cyclic quadrilateral
∴ ∠ABC + ∠AEC = 180°
(pair of opposite angles in a cyclic quadrilateral are supplementary)
⇒ ∠ABC =180° - 45° =135°
Similarly, ∠CDE = 135°
∴ ∠ABC + CDE -135° +135° = 270°