Question

In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.

Answer 1

Join AC and BD

∴ ∠CAD = 90° and ∠CBD = 90°

(Angle in a semicircle is a right angle)

Also, AB || CD

∴ ∠BAD = ∠ADC = 25°  ...(Alternate angles)

∠BAC = ∠BAD + ∠CAD

= 25° + 90°

= 115°

∴ ∠ADB = 180° – 25° – ∠BAC

= 180° – 25° – 115°

= 40°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

Also, ∠AEB = ∠ADB = 40°

(Angle subtended by the same chord on the circle are equal)