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°.
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
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1 answer