In a right triangle, one of the angles measures 90°. The sum of the angles in any triangle is always 180°.
If one angle is 36° and the right angle is 90°, we can find the third angle by subtracting the sum of the known angles from 180°:
\[ \text{Third angle} = 180° - (90° + 36°) = 180° - 126° = 54°. \]
So, the measure of the third angle is 54°.