SOLUTION: find the no of sides of regular convex polygon whose angle is 40 deg?

Question 33843: find the no of sides of regular convex polygon whose angle is 40 deg?

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
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.
RELATED QUESTIONS
The measure of an interior angle of a regular polygon is given- 135 Deg. Find the number... (answered by Fombitz)

Find the number of sides in a regular convex polygon where each interior angle measures... (answered by Alan3354)

An interior angle of a regular convex polygon measures 144 degress how many sides does... (answered by solver91311,Earlsdon)

Each interior angle of a regular convex polygon measures 156�. How many sides does the... (answered by Alan3354)

THE INTERIOR ANGLE ME A REGULAR CONVEX POLYGON IS 156 . HOW MANY SIDES HAS THE... (answered by ikleyn,Alan3354)

find the number of sides of a regular polygon whose interior angle is twice the exterior... (answered by 10037376,Alan3354)

What is the sum of the measures of the exterior angles of any convex polygon, one angle... (answered by vleith)

find the number of sides of a convex polygon whose sum of the measures of its interior... (answered by psbhowmick)

one exterior angle of a convex polygon is 40 degree and each of the others is equal to 20 (answered by richard1234)