A regular decagon has 10 sides of equal length. What is the measure, in degrees, of one ex… — ACT

A regular decagon has $10$ sides of equal length. What is the measure, in degrees, of one exterior angle of this decagon?

Answer: 36 degrees

The correct answer is 36.

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

360^\circ

. A regular decagon has

10

congruent sides and therefore

10

congruent exterior angles. Dividing

360^\circ

10

yields

36^\circ

for each exterior angle.

Determine the number of exterior angles in a regular decagon.

A decagon has 10 sides, so it has 10 exterior angles.

A polygon has the same number of exterior angles as its number of sides.

State the sum of the exterior angles for a convex polygon.

The sum of the exterior angles is 360 degrees.

The exterior angles of any convex polygon always sum to 360 degrees regardless of the number of sides.

Calculate the measure of one exterior angle.

360 / 10 = 36

Since the decagon is regular, all of its exterior angles are equal in measure, so we divide the total sum by the number of angles.

The sum of the exterior angles of any convex polygon is

360^\circ

. For a regular polygon with

n

sides, the measure of each exterior angle is

\frac{360^\circ}{n}

Question