How many regular polygons with number of sides 'n' exist such that all the angles (in degrees) of the polygon are integers?
Explanation:
We know sum of all interior angles of a polygon = (n - 2) × 180°
∴ Each interior angle of a regular polygon = n-2×180°n=180°-360°n.
Now for interior angles to be integer, 360°n should be an integer i.e., n should be a factor of 360 and greater than 2.
Total factors of 360 = 24
Regular Polygons satisfying the conditions specified above are 22 (n > 2).
Hence, 22.
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