What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?

I believe the answer is 11.24 units.

If you are given an isosceles triangle with a vertex angle of 38 degrees, that would tell you that the other angles in the triangle are both 71 degrees. 

In this case, I would use ratios of an angle to it's opposite side. Therefore, we would have: (38°)/X = (71°)/(21 units)

Now you can solve for X, algebraically, and the answer I got was 11.24 units.

The correct answer is: 2