If an isosceles triangle has a base angle measuring 40 degrees then what measure is the vertex angle

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**.

Would you like more details or have any questions?

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.

Learn how to find the vertex angle in an isosceles triangle with each base angle measuring 40 degrees. This problem demonstrates the angle sum property in triangles and is suitable for students in Grades 6-8.

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