The sum of the interior angles of a regular polygon is 1080°. Calculate the number of sides and the size of each exterior angles of the polygon

Answer 1

To find the number of sides of the regular polygon, we can use the formula for the sum of the interior angles:

Sum of interior angles = (n-2) * 180°

Given that the sum of the interior angles is 1080°, we can set up the equation:

1080 = (n-2) * 180
1080 = 180n - 360
1440 = 180n
n = 8

Therefore, the regular polygon has 8 sides.

To find the size of each exterior angle, we can use the formula:

Exterior angle = 360° / n

Substitute n = 8 into the formula:

Exterior angle = 360 / 8
Exterior angle = 45°

Therefore, each exterior angle of the regular polygon is 45°.