What is the Base?

It is not given if the angle of $100^\circ$ is a vertex or base angle.

If it was a base angle, then there are 2 angles which sum up to $200^\circ$ , contradicting the fact that angles in a triangle sum up to $180^ \circ$ . Hence, it must be a vertex angle. As such, the base angle is $\frac {180^ \circ - 100^ \circ} { 2} = 40 ^ \circ$ .