To find the angle $x$, let's analyze the given geometric figure step by step.

1. Given Information:

   • $\triangle ABC$ is an isosceles triangle with $AB = AC$.
   • $\angle ABC = \angle ACB = x$.
   • $\angle BAC = 75^\circ$.
   • $D$ is a point on $BC$ such that $AD$ bisects $\angle BAC$.

2. Isosceles Triangle Property:

   • In an isosceles triangle, the base angles are equal.
   • Therefore, $\angle ABC = \angle ACB = x$.

3. Sum of Angles in $\triangle ABC$:

   • The sum of angles in a triangle is $180^\circ$.
   • $\angle BAC + \angle ABC + \angle ACB = 180^\circ$.
   • Given that $\angle BAC = 75^\circ$ and $\angle ABC = \angle ACB = x$, we have: $75^\circ + x + x = 180^\circ$ $75^\circ + 2x = 180^\circ$ $2x = 180^\circ - 75^\circ$ $2x = 105^\circ$ $x = 52.5^\circ$

Therefore, the angle $x$ is $52.5^\circ$.

Would you like more details or have any other questions?

Here are some questions you might want to ask:

1. Can you explain the properties of isosceles triangles in more detail?
2. How do you determine the sum of angles in a triangle?
3. What are the steps to bisect an angle in a triangle?
4. Can you solve for angles in other types of triangles, like equilateral or scalene?
5. How do you use angle bisectors in solving geometric problems?

Tip: Always check the properties of triangles and their internal angles when solving geometric problems.