Each exterior angle of a regular polygon measures 24^\circ. How many sides does this polyg… — JAMB UTME

Each exterior angle of a regular polygon measures $24^\circ$ . How many sides does this polygon have?

Answer: 15 sides

The polygon has 15 sides.

The sum of all exterior angles of any convex polygon is always

360^\circ

. Because the polygon is regular, all its exterior angles are equal. Dividing

360^\circ

by the measure of one exterior angle (

24^\circ

) yields exactly 15 sides.

Identify the formula relating exterior angle and number of sides

The sum of exterior angles of any convex polygon is

360^\circ

. For a regular polygon with

n

sides, each exterior angle equals

\frac{360^\circ}{n}

All exterior angles in a regular polygon are equal.

Rearrange the formula to solve for the number of sides

n

n = \frac{360^\circ}{\text{Exterior Angle}} = \frac{360^\circ}{24^\circ} = 15

Dividing the total sum of exterior angles by the measure of one exterior angle yields the total number of sides.

Exterior angle property of regular polygons

Question