We are given a triangle with one angle measuring $42^{\circ}$. We are asked to find the measure of the angle labeled $c$. The angle $c$ appears to be an exterior angle to the triangle. We are also given a number 97. I assume it is asking for $c$ degrees.

1. Problem Description

We are given a triangle with one angle measuring $42^{\circ}$. We are asked to find the measure of the angle labeled $c$. The angle $c$ appears to be an exterior angle to the triangle. We are also given a number

9

7. I assume it is asking for $c$ degrees.

2. Solution Steps

The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Since the angle $c$ is an exterior angle, we need to find the two non-adjacent interior angles. One of the angles is $42^{\circ}$. The other interior angle is not given in the picture.

Based on the figure, it seems that angle $c$ is supplementary to one of the angles in the triangle. Let that angle be $x$. Then, $x + c = 180$. Also, the sum of the three angles in a triangle is

1

8

0. Let the other interior angle be $a$. Then $42 + x + a = 180$.

Also, $c = 42 + a$

$a = c - 42$

Substituting $a = c - 42$ into $42 + x + a = 180$, we have

$42 + x + c - 42 = 180$

$x + c = 180$.

Therefore, $x$ and $c$ are supplementary angles.

It looks like the exterior angle is $97^{\circ}$. Thus $c = 97$.

Then $x = 180 - c = 180 - 97 = 83$.

Also, $a = c - 42 = 97 - 42 = 55$.

The sum of the angles in the triangle is $42 + 83 + 55 = 180$.

3. Final Answer

The value of $c$ is

9

7.