In this image, we see a triangle where two sides are marked as congruent (indicated by the hash marks), making this an isosceles triangle.

The angles opposite these congruent sides are also congruent. One angle is labeled as $32^\circ$, and the other is labeled as $x + 4$.

To find the value of $x$, follow these steps:

1. Since the sum of the interior angles in any triangle is always $180^\circ$, we can write the equation:

   $32^\circ + (x + 4)^\circ + (x + 4)^\circ = 180^\circ$

2. Simplify the equation:

   $32^\circ + 2(x + 4) = 180^\circ$

   $32^\circ + 2x + 8 = 180^\circ$

3. Combine like terms:

   $40^\circ + 2x = 180^\circ$

4. Subtract 40 from both sides:

   $2x = 140^\circ$

5. Finally, divide by 2:

   $x = 70^\circ$

So, the value of $x$ is 70 degrees.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the sum of all interior angles in a quadrilateral?
2. How do you find the missing angle in a right triangle?
3. How does knowing that a triangle is isosceles help solve problems?
4. What are the properties of an equilateral triangle?
5. Can an isosceles triangle have a right angle?

Tip: Always remember that the sum of interior angles in any triangle is $180^\circ$, which is useful when solving problems involving triangles.