The diagram shows a triangle with an angle of $32^\circ$ and two angles marked as equal by the tick marks. This indicates that the triangle is isosceles, where two sides are of equal length and, therefore, their opposite angles are equal.

To solve for $x$:

1. Sum of angles in a triangle: The sum of the internal angles of any triangle is always $180^\circ$.

2. Let the two equal angles be $x^\circ$: Since it's an isosceles triangle, the two base angles are equal.

3. Set up the equation: $x + x + 32^\circ = 180^\circ$ Simplifying: $2x + 32^\circ = 180^\circ$ Subtract 32 from both sides: $2x = 148^\circ$ Divide by 2: $x = 74^\circ$

So, the value of $x$ is $74^\circ$.

Would you like a more detailed explanation or have any questions? Here are five related questions:

1. How do you determine if a triangle is isosceles from a diagram?
2. What is the sum of the interior angles of any polygon?
3. How can you find the third angle of a triangle if you know the other two?
4. Why are the base angles in an isosceles triangle always equal?
5. How do angle relationships help solve real-world problems?

Tip: Always remember that in an isosceles triangle, the angles opposite the equal sides are equal!