xxallifratxx
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If each interior angle of a regular polygon contains 162º, find the number of sides of the polygon. Help??
Interior Angles
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Do you know a formula that tells you the sum of interior angles for a polygon of n sides?If each interior angle of a regular polygon contains 162º, find the number of sides of the polygon. Help??
For a triangle, n=3 and sum = 180°
For a quadrilateral, n=4 and sum = 360°
--> each time n increases by 1, the sum of interior angles increases by 180°
--> sum of interior angles = (n - 2)×180°
[The actual proof of this theorem involves dividing the polygon into n triangles.]
You are given that each angle is 162°, so the sum of angles is n×162° (where n is the number of sides).
If you set those two expressions for the sum of interior angle equal, you should be able to solve for n.
If each interior angle of a regular polygon contains 162º, find the number of sides of the polygon. Help??
You've already been shown ONE approach to this problem. Here's another.
Since you are told that the polygon is REGULAR, you should recall that each of the interior angles has the same measure. Each of the exterior angles must have the same measure as well, since the interior angle and exterior angle at one vertex are supplementary.
If you know that an interior angle has a measure of 162 o, what would be the measure of an exterior angle at that same vertex?
Another important fact that will help with this kind of problem is knowing that the sum of the exterior angles (one at each vertex) of ANY polygon is always the same....do you know what that sum is?
Ok...now if you know that you have "n" exterior angles, all with the same measure, and you know what the sum of those "n" angle measures is, can you see a simple way to determine how many of those angles you have? And the number of sides is the same as the number of angles in the n-sided regular polygon.
It is often easier to work with the sum of the exterior angles of a regular polygon because the sum of the exterior angles is always the same, regardless of the number of sides the polygon has.