Respuesta :
Answer:
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 = [tex]\frac{360^{\circ}}{n}[/tex] 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 = [tex]\frac{360^{\circ}}{5} =72^{\circ}[/tex]
Therefore, the measure of one of the central angle in the regular pentagon is, [tex]72^{\circ}[/tex]
