The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

Solution:

The information presented in the problem statement is summarised in the diagram below:

An isosceles triangle is a three sided polygon which has two sides equal.

Since the two sides are equal the angles opposite those sides are also equal.

In the above diagram:

AB = AC and 

∠ABC = ∠ACB = 54°

We also know that sum of the angles of a triangle is 180°.

∠ABC + ∠ACB + ∠BAC = 180°

54° + 54° + ∠BAC =180°

108° + ∠BAC =180°

∠BAC = 180° - 108° = 72°

The vertex angle is 72°.

The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?

Summary:

The base angle of an isosceles triangle measures 54 °. The measure of its vertex angle is 72°.