The vertex angle of an isoceles triangle 40 degrees less than the sum of the measures of the base angles. determine the measure of the vertex angles.

V = vertex angle
B = base angle

"the vertex angle is 40 degrees less than the sum of the measures of the base angles" means V = B+B-40 which turns into V = 2B-40

Use the fact that the three angles (B, B, V) add up to 180 degrees. Then use substitution to solve for B

V+B+B = 180
V+2B = 180
2B-40+2B = 180
4B-40 = 180
4B = 180+40
4B = 220
B = 220/4
B = 55
Each base angle is 55 degrees

V = 2B-40
V = 2*55-40
V = 110-40
V = 70
The vertex angle is 70 degrees

Check:
V+B+B = 70+55+55 = 180
answer checks out