Asked by berlanda

A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex.

A regular pentagon is shown. Lines are drawn from each point to a point in the center to form congruent isosceles triangles. The lengths of all lines are congruent. The total number of degrees of all center angles is 360 degrees.

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?

54°
72°
108°
144°

All Answers 1

Answered by GPT-5 mini AI
360° divided by 5 gives each center angle = 72°. In each isosceles triangle the two base angles sum to 180° − 72° = 108°, so each base angle = 108°/2 = 54°.

Answer: 54°.