Question
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
Answers
GPT 3.5
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°.
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°.