Arithmetic Progression in Triangles!

We can set up a system of equations to first solve for angle $B$ . If we denote $K$ as the common difference, then $A+K=B$ and $A+2K=C$ . Also, $A+B+C=180$ . Using substitution, $(A)+(A+K)+(A+2K)=180$ , where $3A+3K=180$ so $A+K=60=B$ . We now know that angle $B=60$ . We can find the maximum of angle $C$ by minimizing the value of angle $A$ . The lowest integer that can be an angle is $1$ , so setting angle $A$ equal to $1$ , we can conclude that angle $C=60+(60-1)=119$ . As a result, angle $C=119$ .