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Remember that the internal angle of a regular convex polygon is (n - 2) * 180 degrees / n, where n is the number of sides in the polygon.
Also remember that the external angle of a regular convex polygon is 180 degrees minus the internal angle a polygon.
So the external angle of a polygon is 180 - ((n - 2) * 180 / n). The sum of the angles will be the external angle multiplied by n, or:
(180 - ((n - 2) * 180) / n ) * n =
180 * n - (n - 2) * 180
Please note that I only proved this for regular polygons, but this formula should also extend to irregular convex polygons too. If a teacher asks you for a proof, then this will be insufficient.
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Why do All polygons have exterior angles that sum to 360 degrees?
Only convex man, if the angle is concave it would not be 360 degree.
How many ways can you find the sum of measures of the exterior angles of a polygon?
The sum of a regular polygons exterior angles always = 360
What is the sum of the exterior angles of a non convex polygons?
The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.The sum is always 360 degrees. Note, though, that when the interior angle is convex, the measure of the exterior angle is negative.
What is the sum of the exterior angles in a convex figure with three sides?
The sum of the exterior angles of any polygon - no matter how many sides, no matter whether it is convex or concave - is 360 degrees.
What polygons sun of its interior angles is exactly the same as the sum of its exterior angles?
no ,is different .
