In figure, `angleADC=130^(@)" and chord BC=chord BE. Find "angleCBE`.

Explanation

We have, `angleADC=130^(@)` and chord BC=chord BE. Suppose, we consider the points A, B, C and D form a cyclic quadrilateral.
Since, the sum of opposite angles of a cyclic quadrilateral ADCB is ` 180^(@)`.
`:. angleADC+angleOBC=180^(@)`
`rArr 130^(@)+angleOBC=180^(@)`
`rArr angleOBC=180^(@)-130^(@)=50^(@)`
`"In" DeltaBOC and DeltaBOE`,
BC=BE [given equal chord]
OC=OE [both are the radius of a circle]
and OB=OB [common side]
`:. DeltaBOC cong DeltaBOE` [by SSS songruence rule]
`rArr angle OBC=angleOBE=50^(@)` [by CPCT]
Now, `angleCBE=angleCBO+angleEBO`
`=50^(@)+50^(@)=100^(@)`