Final answer:
In an isosceles triangle with a vertex angle of 30 degrees, each base angle measures 75 degrees since the total degrees in a triangle add up to 180 and the base angles are equal.
Step-by-step explanation:
When considering the angles of a triangle, we know that a triangle has three interior angles that always add up to 180 degrees. Given that the isosceles triangle has one vertex angle that measures 30 degrees, the remaining 150 degrees must be divided equally between the two base angles because an isosceles triangle has two equal sides, and therefore, two equal angles.
The measure of each base angle is therefore 150 degrees divided by 2, which is 75 degrees each. Hence, the correct answer to the question is A. 75 degrees.