Answer
49 degrees
Work Step by Step
We call the measure of C equal to x. We call the measure of CEB y. We call the measure of angle EBG z. Since the sum of angles is always 180 degrees for a triangle, we find:
$$ .5x+121+z=180 \\ .5x+y+59=180 \\ 2z+y-108+x=180$$
Solving, we find that the measure of angle C is $\frac{98}{2} = 49^{\circ}$
