The relation of a right angle vertices interior and exterior is 1:4. Where we can work with other ratio that does not have right angles, if comparing an exterior angle to an interior angle where a ratio 1:3 is found- how many sides does the polygon have.

The picture just shows the beginning logic. We now know that we need to find a polygon with an interior angle that has a ratio of 1:3 with its exterior angle.

We can use this formula to find the number of sides of the polygon:

((n-2)×180)/n = 120

(n-2)×180 = 120n

180n - 360 = 120n

60n = 360

n = 6

We now know that the shape has 6 sides with 120 degree interior angles.

A shape with 6 sides is a hexagon.

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