#### Question

In the given figure, AE is the diameter of the circle. Write down the numerical value of ∠ABC+∠CDE. Give reasons for your answer.

#### Solution

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°

Is there an error in this question or solution?

Solution In the Given Figure, Ae is the Diameter of the Circle. Write Down the Numerical Value of ∠Abc+∠Cde. Give Reasons for Your Answer. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.