ABCDE is a cyclic pentagon with centre of its circumcircle at point O such that AB = BC = CD and angle ABC = $120^{o}$ .

Calculate :

(i) $∠$ BEC (ii) $∠$ BED

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Solution

Traingle AOB,DOC and COB are equilateral traingle as OA = OD = OC = OB all are radii of the circle and AB = BC = CD so all the 3 sides of all the 3 triangles are equal so by SSS Test All the 3 triangles are congruent
So,
∠AOB = ∠DOC = ∠COB [By C.P.C.T.C]

∠OBA + ∠OBC = 120

2∠OBA = 120

∠OBA=60

and

∠OCD + ∠ODC + ∠COD = 180

120 + ∠COD = 180

∠COD =60

(i) ∠BEC = 0.5 ∠BOC = 30

(ii)∠BED = 0.5 ∠BOD = 60

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