The image shows a triangle with one angle labeled as $42^{\circ}$. The problem asks to find the angle 'c'. It is assumed that 'c' refers to the angle at the bottom right of the triangle. The triangle appears to be isosceles, meaning two of its sides are equal. If the triangle is isosceles, then the two angles opposite the equal sides are also equal.

1. Problem Description

The image shows a triangle with one angle labeled as $42^{\circ}$. The problem asks to find the angle 'c'. It is assumed that 'c' refers to the angle at the bottom right of the triangle. The triangle appears to be isosceles, meaning two of its sides are equal. If the triangle is isosceles, then the two angles opposite the equal sides are also equal.

2. Solution Steps

Step 1: Assume the triangle is isosceles.

If the triangle is isosceles, then the angle opposite the side adjacent to the $42^{\circ}$ angle is also $42^{\circ}$. Let the three angles of the triangle be $A$, $B$, and $C$. We are given that $A = 42^{\circ}$. If the triangle is isosceles, then $B = 42^{\circ}$.

Step 2: Calculate the third angle.

The sum of the angles in a triangle is $180^{\circ}$.

$A + B + C = 180^{\circ}$

$42^{\circ} + 42^{\circ} + C = 180^{\circ}$

$84^{\circ} + C = 180^{\circ}$

$C = 180^{\circ} - 84^{\circ}$

$C = 96^{\circ}$

Step 3: Determine if the assumption holds.

If the triangle is isosceles and the angle at the top is $42^{\circ}$, then the base angles are equal, and their sum is $180^{\circ} - 42^{\circ} = 138^{\circ}$. Each base angle would be $138^{\circ}/2 = 69^{\circ}$. However, the number next to the triangle on the image is 97, so angle C is equal to $97^{\circ}$. Let's calculate what that makes the third angle.

Step 4: Recalculate the unknown angle.

$42^{\circ} + C = 180^{\circ} - B$

Since the value 97 seems to be closer to $C$, let us assume $C=97^{\circ}$. Then $42^{\circ} + B + 97^{\circ} = 180^{\circ}$

$B = 180^{\circ} - (42^{\circ} + 97^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}$

Thus angle C is $97^{\circ}$

3. Final Answer

96