Polygon interior angle calculator
The exterior angles of any polygon sum to a full turn, which is where every other formula here comes from.
Interior angle
135.000 000degrees
- Exterior angle
- 45.000 000 degrees
- Sum of interior angles
- 1080 degrees
- Number of diagonals
- 20
- Triangles it divides into
- 6
- Central angle
- 45.000 000 degrees
Show the working
- Number of sides = 8
- Sum of interior angles = (8 - 2) * 180 = 1080
- Interior angle = 1080 / 8 = 135
- Exterior angle = 360 / 8 = 45
- Number of diagonals = 8 * (8 - 3) / 2 = 20
- Triangles it divides into = 8 - 2 = 6
- Central angle = 360 / 8 = 45
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- sum of interior angles = (n - 2) x 180 degrees
- each interior angle of a regular polygon = (n - 2) x 180 / n
- diagonals = n(n - 3) / 2