Question

The sum of each 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

[AI-generated answer — Bot GPT 3.5]

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

Sum of interior angles = (n-2) * 180°

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

1080 = (n-2) * 180
6 = n-2
n = 8

Therefore, the regular polygon has 8 sides.

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

Size of exterior angle = 360° / n

Substituting n = 8 into the formula, we get:

Size of exterior angle = 360° / 8
Size of exterior angle = 45°

Therefore, the regular polygon has 8 sides and each exterior angle measures 45°.