Answer
The sum of the three angles of a triangle add to $180^{\circ}$, and angle $ABD = 150^{\circ}$. Therefore the sum of angle $BAD$ and angle $BDA$ add to $30^{\circ}$
Since triangle $ABD$ is an isosceles triangle and $AB = BD$, then angle $BAD$ is equal to angle $BDA$.
Therefore, angle $BDA = 15^{\circ}$, and angle $BAD = 15^{\circ}$
Work Step by Step
$AB$ is a radius of the circle and $BD$ is a radius of the circle. Therefore, $AB = BD$.
In the triangle $ABD$, since the two sides $AB$ and $BD$ are equal, the triangle $ABD$ is an isosceles triangle.
The sum of the three angles of a triangle add to $180^{\circ}$, and angle $ABD = 150^{\circ}$. Therefore the sum of angle $BAD$ and angle $BDA$ add to $30^{\circ}$
Since triangle $ABD$ is an isosceles triangle and $AB = BD$, then angle $BAD$ is equal to angle $BDA$.
Therefore, angle $BDA = 15^{\circ}$, and angle $BAD = 15^{\circ}$
