https://file.aiquickdraw.com/mathbot/file/1725430891219cosued3k.jpg

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!

Solve the problem of finding the missing angle in a triangle where two angles are given as 42° and 117°. Learn how to apply the Triangle Sum Theorem to determine the third angle, suitable for students in Grades 6-8.

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