ABCD is a cyclic quadrilateral.
We know that sum of opposite angles of cyclic quadrilateral is 180°
∴ ∠ADC + ∠ABC = 180°
⇒ ∠ABC = 180° – ∠ADC
⇒ ∠ABC = 180° – 130°
⇒ ∠ABC = 50°
⇒ ∠OBC = 50°
In ΔBCO and ΔBEO
BC = BE (given)
∠BCO = ∠BEO [Angles opposite to equal sides]
BO = BO (common)
∴ By SAS congruence
ΔBCO = ΔBEO
∴ ∠OBC = ∠OBE
∴ ∠OBE = 50° [∠OBC = 50°]
Now ∠CBE = ∠CBO + ∠OBE
= 50° + 50°
= 100°
Thus ∠CBE = 100°
