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Q: How many ways can you find the sum of measures of the exterior angles of a polygon?

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Measure them with a protractor

For any n-sided regular polygon the exterior angles are 360/n degrees.

if the exterior angle is 40 degrees the interior angle of the polygon is 180- 40 = 140 degrees. The equation for sides N is interior angle = 180 x (N-2)/N; solving you find N = 9 sides

8 Since the sum of the exterior angles of any polygon is always 360, you can divide 360 by 45 to find the number of exterior angles, which is 8. That means 8 interior angles and eight sides as well.

Yes and here is why. The sum of the exterior angles of a regular polygon of n sides is 360°. Each exterior angle measures 360°/n. So we need to find a natural number n such that 360/n=30 and that n will be the number of angles in the polygon. 360/n=30 360=30n 360/30=n so n would need to be 12 and a 12 sided regular polygon has each exterior angle of measure 30 degrees.

Related questions

The exterior angles of any polygon add up to 360 degrees.

If it's a regular polygon: 360/number of sides = each exterior angle

The exterior angles of any polygon add up to 360 degrees

The exterior angles of any polygon add up to 360 degrees

The exterior angles of any polygon always add up to 360 degrees

The sum of the exterior angles of any polygon is 360 degrees.

Use a protractor

The sum of exterior angles, of any polygon - convex or concave, and whatever the number of sides - is 360 degrees or 2*pi radians.

The exterior angles of any polygon add up to 360.

Measure them with a protractor

A regular polygon with interior angles measuring 165 degrees each will have exterior angles measuring 15 degrees each, since each pair of interior/exterior angles forms a linear pair whose measures total 180 degrees. For any polygon, the sum of the exterior angles is 360 degrees. You can find how many sides, and therefore vertices, in the polygon by dividing 360 by 15. In this case, the polygon has 360/15 = 24 sides.

For any n-sided regular polygon the exterior angles are 360/n degrees.

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