MathematicsIn the figure ∠ADC=130oand chord BC = chord BE. Then, which of the following is the measure ∠CBO?

In the figure $∠ ADC = 130^{o}$ and chord BC = chord BE. Then, which of the following is the measure $∠ CBO$ ?

Consider the given figure,

From the figure,

ABCD

is a cyclic quadrilateral. Also,

∠ ADC = 130^{o}

and chord BC = chord BE.
We know that sum of opposite angles of a cyclic quadrilateral are supplementary.
Then in quadrilateral ADCB,

∠ ADC + ∠ CBA = 180 °

∠ CBA = 180 ° - ∠ ADC

∠ CBA = 180 ° - 30^{o}

∠ CBO = ∠ CBA = 50^{\circ}

Hence, the measure of

∠ CBO

50^{\circ}

.
Therefore, option 2 is correct.

JEE