Question

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

27°
36°
54°
72°

Answer 1

The answer is the last one because in isosceles triangles the base angles are congruent.

Answer 2

The measure of the vertex angle is 72 degrees

Isosceles triangle

The sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;

54 + 54 + x = 180

where

x is the vertex angles

Simplify

108 + x = 180

x = 180 - 108

x = 72 degrees

Hence the measure of the vertex angle is 72 degrees

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