Mathematics
In the figure given alongside, AB || CD and O is the center of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.
Circles
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Answer
Join AC, BD and CB.
As angle is a semicircle is a right angle.
∴ ∠CAD = 90° and ∠CBD = 90°
Given, AB || CD
So, ∠BAD = ∠ADC = 25° [Alternate angles are equal]
From figure,
∠BAC = ∠BAD + ∠CAD = 25° + 90° = 115°.
Sum of opposite angles in a cyclic quadrilateral = 180°.
In quadrilateral ACDB,
⇒ ∠CDB + ∠BAC = 180°
⇒ ∠CDA + ∠ADB + ∠BAC = 180°
⇒ 25° + ∠ADB + 115° = 180°
⇒ ∠ADB = 180° - 115° - 25° = 40°.
As angles in same segment are equal.
∴ ∠AEB = ∠ADB = 40°.
Hence, ∠AEB = 40°.
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