Question

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

Answer 1

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In isosceles triangle two side are equal, therefore AB = AC

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Answer 2

Given - Base angle of isosceles triangle = 54°

Find - Measure of vertex angle

Solution - The isosceles triangle has two sides equal. Thus, two base angles of isosceles triangle will also be equal. Further, we know sum of all angles of triangle is 180°. Now, using these facts to find out vertex angle.

Let the vertex angle be x.

54° + 54° + x = 180°

108° + x = 180°

x = 180° - 108°

x = 72°

Therefore, the measure of vertex angle of given isoceles triangle is 72°.