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Find the number of sides of a regular convex polygon whose
angle
is 40degrees.
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Answer / tanuj sinha
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
| Is This Answer Correct ? | 20 Yes | 2 No |
Answer / jjjj
If it's the internal angle, then the external angle is 180-40 = 140 and 140n = 360 => no solution since n must be an integer.
If it's the external angle, then 40n = 360 => n = 9 so the number of sides is 9
...
| Is This Answer Correct ? | 12 Yes | 3 No |
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