Use this regular pentagon to answer the questions. what is the measure of one of the central angles in the regular pentagon?

Measure of one of the central angles in the regular pentagon is 72 degree.

Step-by-step explanation:

A Central angle states that the angle made at the center of the polygon by any two adjacent vertices of the polygon.

If you draw a line from any two adjacent vertices to the center, then they would make the central angle.

Since, it is given that the polygon we use here is regular pentagon.

⇒ All the central angles are equal.

The formula to find the central angle is:

Central Angle = where n is the number of sides.

Since, the measure of the central angle thus depends only on the number of sides.

Here, side(n) = 5 (Polygon is regular pentagon)

then;

Central angle =

Therefore, the measure of one of the central angle in the regular pentagon is,