The image shows a triangle with its angles labeled: one angle is $42^\circ$, another is $117^\circ$, and the third angle, labeled $c$, is unknown.

To find the value of $c$, we use the fact that the sum of the interior angles in any triangle is $180^\circ$.

The formula is:

$c = 180^\circ - (42^\circ + 117^\circ)$

Calculating this:

$c = 180^\circ - 159^\circ = 21^\circ$

Therefore, the value of $c$ is:

$\boxed{21^\circ}$

Would you like more details or have any questions? Here are some related questions to explore further:

1. What is the sum of the interior angles of any polygon?
2. How do you find an unknown angle in a triangle if two angles are given?
3. What properties do the angles of a triangle have?
4. How can you identify an obtuse triangle based on its angles?
5. How would this problem change if it were a right triangle?

Tip: Remember that the sum of the angles in any triangle is always $180^\circ$, which is a useful property for solving many geometric problems!