We are given a triangle with two angles: $\angle A = 72^\circ$ and $\angle B = 55^\circ$, and we are asked to find the measure of $\angle C$.

In a triangle, the sum of the angles is always $180^\circ$. Therefore, we can find $\angle C$ using the equation:

$\angle A + \angle B + \angle C = 180^\circ$

Substituting the known values:

$72^\circ + 55^\circ + \angle C = 180^\circ$

Simplifying:

$127^\circ + \angle C = 180^\circ$

Now, subtract $127^\circ$ from both sides:

$\angle C = 180^\circ - 127^\circ = 53^\circ$

Thus, the measurement of $\angle C$ is $53^\circ$, which corresponds to option D.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the sum of the angles in any polygon with more than three sides?
2. How do you classify triangles based on their angles (acute, obtuse, right)?
3. What is the relationship between the side lengths and angles of a triangle?
4. How would the problem change if one of the given angles were $90^\circ$?
5. Can a triangle have two angles that are greater than $90^\circ$?

Tip: In any triangle, always remember that the sum of the interior angles is exactly $180^\circ$, which can help you solve for missing angles easily.