Question

The given figure shows a Pentagon inscribed in a circle with centre O.Given AB=BC=CD and angle ABC=132°

Answer 1

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]