⟩ Find the number of sides of a regular convex polygon whose angle is 40degrees?
The measure of one vertex angle of a regular polygon is given by:
where n is the number of sides of the regular polygon...and, of course, it goes without saying, that n must be an integer >2(i.e, 3, 4, 5, 6, ...).
If the measure of one vertex angle of a regular polygon is 40 degrees, then we can write:
Simplify and solve for n.
Multiply both sides by n.
Add 360 to both sides.
Subtract 40n from both sides.
Divide both sides by 140.
This is not possible since a regular polygon must have an integral numer of sides.
Conclusion:
There is no regular polygon whose vertex angle is 40 degrees
