We are given a triangle ABC with angle A = $63^\circ$ and angle B = $42^\circ$. We need to find the measure of angle C.

1. Problem Description

We are given a triangle ABC with angle A = $63^\circ$ and angle B = $42^\circ$. We need to find the measure of angle C.

2. Solution Steps

The sum of the angles in a triangle is always $180^\circ$. Therefore, we have the equation:

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

We are given that $A = 63^\circ$ and $B = 42^\circ$. Substituting these values into the equation, we get:

$63^\circ + 42^\circ + C = 180^\circ$

$105^\circ + C = 180^\circ$

Subtracting $105^\circ$ from both sides, we find:

$C = 180^\circ - 105^\circ$

$C = 75^\circ$

3. Final Answer

The measure of angle C is $75^\circ$.