Final answer:
The vertex angle of an isosceles triangle with base angles of 75 degrees each is 30 degrees, calculated by subtracting the combined base angles from the total of 180 degrees in a triangle. The correct answer is b.
Step-by-step explanation:
When considering the properties of a triangle, it is crucial to remember the fundamental rule that the sum of the angles in any triangle is 180 degrees. An isosceles triangle is defined by having two sides that are equal in length, and correspondingly, two angles that are equal, which are known as the base angles. Given that the base angle of the isosceles triangle in question is 75 degrees and there are two base angles, the combined measure of these two angles is 150 degrees (75 degrees times 2).
By subtracting the sum of the base angles from the total sum of the angles of a triangle, we can determine the measure of the vertex angle. With a total sum of 180 degrees for all angles in a triangle, we subtract the combined measure of the base angles:
180 degrees - 150 degrees = 30 degrees
Therefore, the measure of the vertex angle in this isosceles triangle is 30 degrees, making option B) the correct answer.