Please solve this question...

It is given that BA = AC, it means triangle ABC is an isosceles triangle. The two angles inclined on equal and non equal lines are same.
$\angle ABC=\angle ACB=50°$

Using the angle sum property of triangle,

$$\begin{gathered} \angle ABC+\angle ACB+\angle BAC=180° \\ 50°+50°+\angle BAC=180° \\ \angle BAC=180°-100° \\ \angle BAC=80° \end{gathered}$$

According to the central angle theorem, the central angle from any two points on the circle is always twice the inscribed angle from those two points.

$$\begin{gathered} \angle BOC=2\times \angle BAC \\ \angle BOC=2\times 80° \\ \angle BOC=160° \end{gathered}$$

Opposite angles of a cyclic quadrilateral are supplementary.

$$\begin{gathered} \angle BAC+\angle BDC=180 \\ \angle BDC=180-80 \\ \angle BDC=100 \end{gathered}$$

Therefore the measure of ∠BOC is 160° and ∠BDC is 100°.

option (a) is correct.