The measure of each exterior angle of a regular 5-gon is less than the measure of each exterior angle of a regular 4-gon.
Step-by-step explanation:
5-gon calculation :
The sum of the angles in a polygon = 180 (n-2) , where "n" is the number of sides of a polygon.
The sum of the angles in a regular pentagon = 180 (5-2) = 180*3 = 540°
The measure of the interior angle of a pentagon = Sum of the angles / n
= 540° / 5 = 108°
The measure of exterior angle of a regular 5-gon = 360° - interior angle
= 360° - 108° = 252°
∴ The measure of each exterior angle of a regular 5-gon is 252°
4-gon calculation :
The sum of the angles in a regular 4-gon = 180 (4-2) = 180*2 = 360°
The measure of the interior angle of a 4-gon = sum of the angles / n
= 360° / 4 = 90°
The measure of exterior angle of a regular 4-gon = 360° - interior angle
= 360° - 90° = 270°
∴ The measure of each exterior angle of a regular 4-gon is 270°
Since, the measure of each exterior angle of a 5-gon is 252° (which is less than 270° the measure of each exterior angle of a regular 4-gon).
