MathematicsIn the given figure, if A, B, C, D are four points such that ∠BAC=30∘. Then, which of the following is the measure of ∠BDC?

In the given figure, if A, B, C, D are four points such that $∠ BAC = 30^{\circ}$ . Then, which of the following is the measure of $∠ BDC$ ?

Consider the given figure,

From the figure- A, B, C, and D are points such that

∠ BAC = 30^{o}

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

∠ BDC = 2 ∠ BAC

∠ BDC = 2 (30^{o})

∠ BDC = 60^{o}

Hence, the measure of

∠ BDC

60^{o}

.
Therefore, option 2 is correct.

JEE