Question

Is it possible to have a regular polygon whose interior angle is 125

Answer 1

Given,

Interior angle = 125°

To Find,

A regular polygon with a given interior angle is possible?

Solution,

Let the side of a regular polygon with this interior angle be x which should be an integer.

All interior angles will be 125° therefore,

Sum of all angles = x * 125 = 125°x

We know by a formula that, the sum of all sides of the polygon = 180° (n - 2)

where n is the number of sides.

Therefore, by equating both equations we get,

125°x = 180° (x -2)

125°x = 180°x - 360°

180°x -125°x = 360°

55°x= 360°

x = 360°/55 = 72°/11

Thus, the value of x is not possible as x should be an integer.

Hence,  it is not possible to have a regular polygon whose interior angle is 125°