Given:
- Triangle ABC
- Exterior angle of the triangle is x = 40°
- Angle B = x
- AB = AC

To Find:
The value of x in triangle ABC.

Solution:

Step 1: Understanding the problem
Let's analyze the given information. We have a triangle ABC, and we know that the exterior angle of the triangle is 40°. We are also given that angle B is equal to x and that AB is equal to AC. Based on this information, we need to find the value of x.

Step 2: Understanding the exterior angle of a triangle
An exterior angle of a triangle is formed by extending one of its sides. In this case, the exterior angle is the angle formed by extending side BC.

Step 3: Using the property of an exterior angle
The property of an exterior angle of a triangle states that it is equal to the sum of the two opposite interior angles. In other words, the exterior angle x is equal to the sum of angles B and C.

Step 4: Applying the property
We know that angle B is equal to x. Therefore, angle C must be equal to 40° - x (as the exterior angle is x = 40°).

Step 5: Using the property of an isosceles triangle
Since AB = AC, triangle ABC is an isosceles triangle. In an isosceles triangle, the base angles (angles opposite to the equal sides) are equal. In this case, angle B and angle C are the base angles.

Step 6: Setting up an equation
Since angle B = angle C, we can set up the equation x = 40° - x.

Step 7: Solving the equation
To solve the equation, we can simplify it by combining like terms. Adding x to both sides, we get 2x = 40°. Dividing both sides by 2, we find x = 20°.

Step 8: Final answer
The value of x in triangle ABC is 20°.

Summary:
To find the value of x in triangle ABC, we used the property of an exterior angle of a triangle, the property of an isosceles triangle, and set up an equation. By simplifying and solving the equation, we found that x is equal to 20°.