Well, to solve for what the angle measures are, simply make the values of angle measures equal to any variable.
So angle A would be X let's say. Also, since angle B would be equal to angle A, then technically since we said that angle A is X, angle B would also be X. For angle C, we have been told that angle C is 2x the measure of angle A which is X, so Angle C would be 2x.
Knowing that the sum of all angles within a triangle add up to 180 degrees, one can easily solve for the variable X and then using the variable X, determine the values of the angle measures.
Angle A + Angle B + Angle C = 180 degrees
X + X + 2X = 180
4X = 180
X = 180/4
X = 45 degrees.
Angle A = 45 degrees
Angle B = 45 degrees
Angle C = 2(45) = 90 degrees.