No, and here's why. It's because:
1. There are n exterior angles of any n-sided polygon.
2. All the exterior angles of any polygon have sum 360°.
3. All exterior angles of a REGULAR polygon are congruent, i.e.,
their measures are all equal.
4. Therefore each exterior angle of an n-sided polygon is 360°/n.
5. So therefore if it were possible to have such a regular polygon,
then each of its exterior angles would be 50°.
6. That would mean that 360°/n = 50°
7. When we solve 360°/n = 50° for n we get:
360° = 50°n
360°/50° = n
360/50 = n
36/5 = n
7 1/5 = n
8. No polygon, regular or not, can have 7 and 1/5th sides.
The number of sides is always a counting number, a positive
whole number or integer.
Edwin
