Question

PLEASE find angle CBE

Answer 1

Given :

In figure ∠ADC = 130° and Chord BC = Chord BE .Find ∠CBE .

Answer :

=>∠ADC = 130°

=> Chord BC = Chord BE

So, ∠ABCD is a cyclic quadrilateral , therefore sum of its opposite angle is 180°

=> ∠ADC + ∠OBC = 180°

=> ∠ADC = 130° , So 130° + ∠OBC = 180°

=> Then, OBC = 50°

Now, in the triangle BOE and BOC

OB = OB ( For reference)

BC = BE ( Given )

OC = OE ( Radios of the circle given in pic )

By the SSS, congruence rule ∆BOC ≈ ∆BOE

∠OBC = ∠OBE = 50°

Now, ∠CBE = ∠CBO + ∠OBE

∠CBE = 50° + 50°

SO, ∠CBE = 100°