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ABCDE is a cyclic pentagon with centre of its circumcircle at point O such that AB = BC = CD and angle ABC = 120°

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ABCDE is a cyclic pentagon with centre of its circumcircle at point O such that AB = BC = CD and angle ABC = 120°

Calculate:

(i) ∠BEC 

(ii) ∠BED

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1 Answer

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Best answer

i) Join OC and OB.

OB and OC are the bisectors of ∠ABC and ∠BCD respectively.

Arc BC subtends ∠BOCat the centre and ∠BEC at the remaining part of the circle.

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