In this problem, we are given a right triangle with one angle measuring $53^\circ$ and the right angle measuring $90^\circ$. We need to find the measure of the third angle.

Solution:

1. In a triangle, the sum of all angles is $180^\circ$.
2. Since one angle is $90^\circ$ (right angle) and another is $53^\circ$, we can find the third angle by subtracting these two from $180^\circ$.

$180^\circ - 90^\circ - 53^\circ = 37^\circ$

Answer:

The measure of the third angle is $37^\circ$.

Would you like more details or have any further questions?

Here are some related questions you might find helpful:

1. How do you find the angles in an isosceles right triangle?
2. What properties distinguish a right triangle from other types of triangles?
3. How do you verify if a triangle is a right triangle given all its angles?
4. What are complementary and supplementary angles, and how do they relate to right triangles?
5. How can you determine the angles of a right triangle if only one non-right angle is given?

Tip: In any triangle, knowing that the angles must add up to $180^\circ$ is a helpful tool for solving unknown angles.