Correct Answer: 105°

Solution : Given: In an isosceles $\triangle ABC$, $AB = AC$.
$\angle BAC=30°$
We know that the sum of all the angles in a triangle is 180°.

In an isosceles $\triangle ABC$, $AB = AC$.
So, $\angle ABC=\angle ACB$
$\angle ABC + \angle ACB + \angle BAC = 180°$
$⇒2\angle ABC + 30° = 180°$
$⇒\angle ABC=\frac{180°–30°}{2}$
$⇒\angle ABC=\frac{150°}{2}=75°$
Since $XY || BC$, $\angle AXY=\angle ABC=75°$
$\angle BXY=180°–\angle ABC$
$⇒\angle BXY=180°–75°$
$⇒\angle BXY=105°$
Hence, the correct answer is 105°.