Question

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

Answer 1

72 and 54 are your answers

Explanation:

Answer 2

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

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

Therefore, the measure of one of the central angle in the regular pentagon is,
`72^(\circ)`