Find out if it is possible with each interior angle equal to 105°

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Solution

The sum of interior angles of a polygon with n sides is 180(n - 2).
This polygon has n angles of 105 degrees or 105n which must equal 180(n - 2). Set them equal and solve for n.
180(n - 2) = 105n
180n - 360 = 105n
75n = 360
n = 360/75 = 4.8
Hence the polygon with each interior angle 105 is not possible.

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