# Requirements Management Question: **Download Questions PDF**

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## Find the number of sides of a regular convex polygon whose angle is 40degrees?

## Answer:

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

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

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