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

54 degrees

Explanation:

.

Answer 2

If all five vertex angles meeting at the center of a regular pentagon are congruent, then each vertex angle of triangle has measure

`(360^(\circ))/(5) =72^(\circ).`

As known the sum of the measures of three triangle angles is 180° and base angles of isosceles triangle are congruent, then the measure of a base angle of one of the triangles is

`(180^(\circ)-72^(\circ))/(2) =(108^(\circ))/(2)=54^(\circ)`.

Answer:
`54^(\circ)`.