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(The exterior angles of a regular polygon total 360 degrees. 360 divided by 40 = 9 sides. For a more difficult way to come up with the same information, read on.)

Okay, this is probably not the most efficient or simple way to do the problem, but I'll show you the way I did it.

First you determine the measure of the interior angles that correspond with the exterior angles. The exterior and interior angles form a straight line. Since a straight line is always 180 degrees:

40+y=180

where y= the measure of any interior angle (they're all the same)

40+y-40=180-40

y=140

so, the interior angles are 140 degrees

Then I wrote a formula to find the total measure of the interior angles of a regular polygon given n sides.

A regular triangle has 180 total degrees, a square has 360, a pentagon has 540, etc.

A formula that works for all of these is:

x=180(n-2)

where n is the number of sides and

where x is the total measure of the interior angles

To get the measure of each angle you simply divide by n, so we now have:

x/n=180*(n-2)/n

I'll replace the x/n with y for simplicity

(y=the measure of each interior angle)

y=180*(n-2)/n

Now simplify the equation to simplest terms

y=180*(n-2)/n

y=180*((n/n)-(2/n))

y=180*(1-(2/n))

y=180-(360/n) (Distributive property)

We have already figured out y from earlier in the problem, so just plug it in and solve for n.

140=180-(360/n)

-40=-360/n

40=360/n

n(40)=(360/n)n

40n=360

n=9

Q: How many sides does a regular polygon with an exterior angle measure of 40 degrees have and how do you do it?

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Providing that it's a regular polygon then each exterior angle will measure 12 degrees.

5 sides and it is a regular pentagon

60 degrees

If the 12-sided polygon is 'regular', then each of its exterior angles is 30 degrees. Whether the polygon is regular or not, all 12 of its exterior angles still add up to 360 degrees, but they may not all be equal.

It is best described as a regular 10 sided polygon or as a regular decagon.

Related questions

A regular polygon will have 360 sides with exterior angles of 181 degrees.

Providing that it's a regular polygon then each exterior angle will measure 12 degrees.

If it's a regular polygon then each exterior angle measures 36 degrees

The sum of the exterior angles of a polygon = 360360 / 36 = 10 degrees

5 sides and it is a regular pentagon

60 degrees

There can be no such polygon. The sum of the exterior angles of ANY polygon is 360 degrees. If it is a regular polygon, then the number of angles MUST divide 360 degrees. Since 18.95 does not divide 360, there cannot be such a polygon. If the exterior angle was 18.94737... degrees, it would be a 19-sided polygon.

The measure of 1 exterior angle of a regular 8-sided polygon is equivalent to 45 degrees. Hope I helped! :)

90 degrees. Exterior angle of any regular n-sided polygon is 360/n degrees

Providing that it is a regular polygon then each exterior angle will measure 12 degrees

The sum of the exterior angles of any irregular or regular polygon is 360 degrees. In this case it is a regular polygon. 360/60 = 6 sides It is a regular hexagon that has 6 equal sides.

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