Final answer:
After setting up an equation accounting for the sum of the angles in a triangle (180 degrees), solving for x, and substituting x back into the expression for the vertex angle, the measure of the vertex angle of triangle ABC is found to be 50 degrees.
Step-by-step explanation:
To find the measure of the vertex angle of an isosceles triangle ABC, we recall that the sum of the angles in any triangle is 180 degrees. In an isosceles triangle, the two base angles are equal, which means if the measure of each base angle is (2x + 17), then the combined measure of the two base angles is 2(2x + 17). The vertex angle, which is given as (x + 26), together with the two base angles must sum up to 180 degrees.
Setting up the equation, we have:
(x + 26) + 2(2x + 17) = 180
Solving for x will allow us to find the precise measure of the vertex angle.
Let's solve the equation:
x + 26 + 4x + 34 = 180
5x + 60 = 180
5x = 120
x = 24
Now we substitute x back into the expression for the vertex angle:
(x + 26)
(24 + 26)
= 50 degrees
Therefore, the measure of the vertex angle of triangle ABC is 50 degrees, which is not one of the options provided: A) 2x + 17, B) x + 26, C) 3x + 43, D) 4x + 43. The options might have been incorrectly stated or a miscalculation has occurred.