The sum of the interior angels of a regular polygon 1800.calculate the size of one exterior angel of the polygon
To calculate the size of one exterior angle of a regular polygon, you need to use the formula:
Exterior Angle = 360° / Number of Sides.
In the case of a regular polygon, all the interior angles are equal. Therefore, to find the size of one interior angle, you need to divide the sum of the interior angles by the number of sides.
Given that the sum of the interior angles is 1800°, and we assume it's a polygon with n sides, the equation becomes:
Sum of Interior Angles = (n - 2) * 180°.
Now, we can solve for n:
1800° = (n - 2) * 180°.
Divide both sides by 180°:
10 = n - 2.
Add 2 on both sides:
n = 12.
Now that we know the number of sides (n = 12) and have the formula for the exterior angle, we can calculate it:
Exterior Angle = 360° / 12.
Exterior Angle = 30°.
Therefore, each exterior angle of the regular polygon is 30°.
sum of angles of any polygon is 180*(n-2) where n is the number of sides in the polygon.
1800/180 = 10, 10+2= 12. there are 12 sides
1800/12 =150 degrees