Final answer:
The measure of angle V in isosceles triangle VWX is found by subtracting the sum of the base angles from 180 degrees. Since the base angles are congruent and less than half of 180 degrees, only one option satisfies this condition, leading to an answer of 82 degrees for angle V.
Step-by-step explanation:
If angle V is the vertex angle of isosceles triangle VWX and sides VX and VW are congruent, then the base angles, angle W and angle X, must be equal. By the properties of triangles, the sum of the interior angles must be 180 degrees. Since angle W is congruent to angle X, we can use the variable x for their measure. This means:
- 2x + m = 180 degrees
- x + x + m = 180 degrees
- 2x = 180 degrees - m
Because VX is congruent to VW, angle V must be strictly greater than angle W and angle X (since it's the vertex angle of the isosceles triangle). There is only one option that is greater than the remaining angles, so the measure of angle V must be 82 degrees, which is the only answer greater than half of 180 degrees but less than 180 degrees itself, as one of the base angles would be.
Thus, the correct answer from the provided choices for the measure of angle V is Option C: 82 degrees.