In the given figure, if ∠ADC= 1300, find ∠ABE.
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⇒ BC=BE [ Given ]
⇒ ∠BCO=∠BEO [ Base angles of equal sides are also equal ]
⇒ BO=BO [ Common side ]
∴ △BCO≅△BEO [ By SAS congruence rule ]
⇒ ∠CBO=∠OBE [ C.P.C.T. ]
Quadrilateral ABCD is a cyclic quadrilateral since, its points lies on a circle.
⇒ ∠ADC+∠CBA=180
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[ Sum of opposite angles of a cyclic quadrilateral is supplementary ]
⇒ 130
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+∠CBA=180
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⇒ ∠CBA=50
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i.e. ∠CBO=50
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∴ ∠OBE=50
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⇒ ∠CBE=50
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+50
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=100
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50degrees
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