The sum of a regular polygons exterior angles always = 360
To find the sum of the measures of the interior angles of a regular polygon with each exterior angle measuring 120 degrees, we first determine the number of sides in the polygon. The sum of exterior angles of any polygon is always 360 degrees, so the number of sides ( n ) can be calculated as ( n = \frac{360}{120} = 3 ). Since it is a triangle, the sum of the interior angles is given by the formula ( (n - 2) \times 180 ) degrees, which for a triangle (3 sides) is ( (3 - 2) \times 180 = 180 ) degrees. Thus, the sum of the measures of the interior angles is 180 degrees.
Measure them with a protractor
For any n-sided regular polygon the exterior angles are 360/n degrees.
if the exterior angle is 40 degrees the interior angle of the polygon is 180- 40 = 140 degrees. The equation for sides N is interior angle = 180 x (N-2)/N; solving you find N = 9 sides
8 Since the sum of the exterior angles of any polygon is always 360, you can divide 360 by 45 to find the number of exterior angles, which is 8. That means 8 interior angles and eight sides as well.
The exterior angles of any polygon add up to 360 degrees.
If it's a regular polygon: 360/number of sides = each exterior angle
The exterior angles of any polygon add up to 360 degrees
The exterior angles of any polygon add up to 360 degrees
The exterior angles of any polygon always add up to 360 degrees
The sum of the exterior angles of any polygon is 360 degrees.
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
The sum of exterior angles, of any polygon - convex or concave, and whatever the number of sides - is 360 degrees or 2*pi radians.
Use a protractor
The exterior angles of any polygon add up to 360.
Measure them with a protractor
For any n-sided regular polygon the exterior angles are 360/n degrees.