for a regular polygon with N sides, sum of all angles equals (180°) * (N - 2)
example: triangle (N = 3): (180°) * (3 - 2) = 180°
square (N=4): (180°) * (4 - 2) = 360°
To find each angle, divide by number of sides: triangle: 180° / 3 = 60°
square: 360° / 4 = 90°
So for a regular 30-gon (N=30): (180°) * (30 - 2) = 5040° (sum of all angles)
and 5040° / 30 = 168° (each angle)
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140 degrees.
Exterior angle = 360/80 = 4.5 degrees. Interior angle = 180 - 4.5 = 175.5 degrees. And, a regular polygon has to be convex.
Exterior angle of a regular 25-gon = 360/25 = 14.4 degrees. So interior angle = 180-14.4 = 165.6 degrees.
The measure of the exterior angle of a convex octagon is indeterminate.
The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.