In an isosceles triangle, the two base angles are equal. If each base angle is 40 degrees, then:

1. The sum of angles in any triangle is 180 degrees.
2. Since both base angles are 40 degrees, their combined measure is $40 + 40 = 80$ degrees.
3. The vertex angle, therefore, will be: $180 - 80 = 100 \text{ degrees}$

So, the measure of the vertex angle is 100 degrees.

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Here are some related questions:

1. What is the vertex angle if each base angle is 50 degrees?
2. How do you find the height of an isosceles triangle if the side lengths are known?
3. What is the relation between the side lengths of an isosceles triangle and its angles?
4. How do angle bisectors divide an isosceles triangle?
5. What are the properties of the altitude from the vertex in an isosceles triangle?

Tip: In any triangle, remember the angle sum property: the angles always add up to 180 degrees.