Question

The adjoining figure shows
a pentagon, inscribed in a
circle with centre O. Given
AB = BC = CD and
ABC = 132º, find:
(i) AEB
(ii) AED
(iii) COD.
​

Answer 1

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In the figure, O is the centre of circle,

with AB = BC = CD.

Also, ∠ABC = 132°

In cyclic quadrilateral,

ABCE ∠ABC + ∠AEC = 180° [sum of opposite angles]

→ ∠132 + ∠AEC = 180°

→ ∠AEC = 180° -132°

→ ∠AEC = 48°

Since, AB = BC, ∠AEB = ∠BEC [equal chords subtends equal angles]

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Answer 2

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