In a right triangle, the sum of the angles is always $180^\circ$. Since one of the angles is $90^\circ$ (the right angle), the sum of the two acute angles must be $90^\circ$.

Given that one acute angle measures $32^\circ$, we can find the other acute angle by subtracting this angle from $90^\circ$:

$90^\circ - 32^\circ = 58^\circ$

Therefore, the measure of the other acute angle is:

58

Would you like further details or have any other questions?

Here are some related questions to explore:

1. How do you calculate angles in any triangle?
2. What are the properties of a right triangle?
3. How do you determine the side lengths in a right triangle if one angle and one side are known?
4. How do you use trigonometric ratios with angles in a right triangle?
5. What is the Pythagorean theorem, and how does it apply to right triangles?

Tip: In a right triangle, the two acute angles will always add up to $90^\circ$.