In this image, we are dealing with a right triangle. One of the angles is given as $59^\circ$, and the angle $a$ is missing. Since the sum of angles in any triangle must be $180^\circ$, and one of the angles is a right angle (i.e., $90^\circ$):

$a + 59^\circ + 90^\circ = 180^\circ$

To find $a$, solve:

$a = 180^\circ - 59^\circ - 90^\circ$ $a = 31^\circ$

Thus, the measure of the missing angle $a$ is $31^\circ$.

Would you like further explanation or details on this? Here are some related questions to deepen your understanding:

1. What is the sum of all interior angles in any type of triangle?
2. How can you confirm the sum of the angles in a right triangle?
3. Can two angles in a triangle be greater than $90^\circ$?
4. How would the calculation change if the given triangle was not a right triangle?
5. How can trigonometry be applied to find unknown sides in this triangle?

Tip: Remember, the sum of the angles in any triangle will always be $180^\circ$, and in a right triangle, one angle is always $90^\circ$.