Question

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles?

Answer 1

Given:

A pentagon

The total number of degrees in the center is 360°

Five congruent isosceles triangles

All five vertex angles meeting at the center are congruent

To find:

The measure of a base angle of one of the triangles

Solution:

To find the vertex of the isosceles triangle,

Central angle / Number of sides

That is,

360 / 5 = 72

To find the sum of the base angles,

180 - Vertex

That is,

180 - 72 = 108

To find the measure of one base angle,

Angle of the sides / 2

That is,

108/2 = 54

The measure of a base angle of one of the triangles is 54 degrees.