MathematicsIn the adjacent figure, if ∠AOC=1100. Then, which of the following is the value of ∠D and ∠B respectively?

In the adjacent figure, if $∠ AOC = 110^{0}$ . Then, which of the following is the value of $∠ D$ and $∠ B$ respectively?

Consider the given figure,

Here,

∠ AOC = 110^{0}

. The angle subtended by a chord to the circumference of a circle is half of that subtended to the centre.
Then,

∠ AOC = 2 ∠ ADC

2 ∠ ADC = 110^{0}

∴ ∠ ADC = 55^{0}

Also, in a cyclic quadrilateral sum of opposite angles are supplementary.
Then in quadrilateral ABCD,

⟹ ∠ B + ∠ D = 180^{0}

⟹ ∠ B + 55^{0} = 180^{0}

⟹ ∠ B = 180^{0} - 55^{0}

⟹ ∠ B = 125^{0}

Hence, the measure of

∠ D

and

∠ B

55^{0}

and

125^{0}

respectively.
Therefore, option 1 is correct.

JEE