In a triangle, the sum of the interior angles always equals $180^\circ$. Given that one angle is $90^\circ$ and another is $13^\circ$, you can find the third angle as follows:

1. Add the two given angles: $90^\circ + 13^\circ = 103^\circ$

2. Subtract the sum from $180^\circ$ to find the third angle: $180^\circ - 103^\circ = 77^\circ$

So, the third angle is $77^\circ$.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What are the properties of a right triangle?
2. How do you calculate the angles of an isosceles triangle if one angle is given?
3. What happens if the sum of two angles in a triangle exceeds $180^\circ$?
4. How do you calculate the angles in an equilateral triangle?
5. What is the exterior angle of a triangle?
6. Can a triangle have two right angles? Why or why not?
7. How do you determine if a triangle is acute, right, or obtuse based on its angles?
8. What are the properties of a triangle with angles $13^\circ$, $77^\circ$, and $90^\circ$?

Tip: Remember, in any triangle, the sum of the angles is always $180^\circ$, a key principle to solve angle-related problems.