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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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What is the measure of each interior angle in a regular convex nonagon?
140 degrees.
What is the measure of one angle of a regular convex 80 gon?
Exterior angle = 360/80 = 4.5 degrees. Interior angle = 180 - 4.5 = 175.5 degrees. And, a regular polygon has to be convex.
What is the measure of one angle of a regular convex 25 gon?
Exterior angle of a regular 25-gon = 360/25 = 14.4 degrees. So interior angle = 180-14.4 = 165.6 degrees.
What is the measure of the exterior angles of a convex octagon?
The measure of the exterior angle of a convex octagon is indeterminate.
What is the sum of the exterior angles of a non convex polygons?
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.
