The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

Solution:

We know that an isosceles triangle has three angles, and their measures add up to 180 degrees.

An isosceles triangle has at least 2 congruent sides, and the angles opposite the congruent sides are congruent.

It is given that the vertex angle of an isosceles triangle measures 40°.

Let us analyse from the figure shown below:

Now let us assume the measure of each base angle is x because the that two angles measure the same.

Using angle sum property of triangle we can write it as:

⇒ x + x + 40 = 180

⇒ 2x + 40 = 180

By transposing we get,

⇒ 2x = 180 - 40

⇒ 2x = 140

Divide both the sides by 2 we get,

⇒ 2x/2 = 140/2

⇒ x = 70

Therefore, the measure of a base angle is 70°.

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

Summary:

If the vertex angle of an isosceles triangle measures 40° then the measure of a base angle is 70°.