Given is the measure of the exterior angles of a regular polygon. How many sides does it have? This probably needs a formula, but unable to find it--I have a lot of homework problems due tomorrow and since I've not taken geometry, I need a lot of help. Thank you, signed Beginner.
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Geometry
- Thread starter kmass7001
- Start date
Picture yourself standing on a giant regular polygon at a vertex. Walk on the perimeter of the polygon. Realize that at each vertex you turn a little bit in order to follow the next side of the polygon. The measure of the angle through which you turn is the measure of an exterior angle. When you have followed the perimeter and are back at the starting point, you have made one complete revolution of 360 degrees. Now, if you measured the number of degrees in each exterior angle, you would realize that if you multiplied the number of exterior angles by the number of degrees in one exterior angle, the product would be 360 degrees.
Hope this helps.
Hope this helps.
kmass7001 said:Given is the measure of the exterior angles of a regular polygon. How many sides does it have? This probably needs a formula, but unable to find it--I have a lot of homework problems due tomorrow and since I've not taken geometry, I need a lot of help. Thank you, signed Beginner.
No matter how many sides a convex polygon has, the sum of the measures of the exterior angles, ONE at each vertex, is 360 degrees.
So, here's an example.
You have a regular polygon (each angle is congruent, and all sides are congruent) with one interior angle equal to 160 degrees. How many sides does this polygon have?
Let n = number of sides in the polygon. If the polygon is regular, each interior angle must have the same measure. If one interior angle is 160 degrees, then EACH interior angle is 160 degrees. An interior angle and an exterior angle at the same vertex must be supplementary...the sum of those angles is 180 degrees. If an interior angle is 160 degrees, then an exterior angle is 180 - 160, or 20 degrees.
Ok...you know that the sum of ALL the exterior angles is 360. You know that one exterior angle is 20 degrees, and you know that ALL of the exterior angles have the same measure (because the polygon is regular.)
There are "n" exterior angles, each has a measure of 20 degrees, and the sum of all of them is 360 degrees.
20n = 360
n = 18
The polygon must have n sides.
There are "x"