How To Determine A Polygon’S Outer Measurement?

The exterior angles of a polygon are formed by extending the sides of the polygon, and the sum total of these angles is always equal to 360°. If the polygon is regular, we can divide 360° for the number of sides to find the measure of an exterior angle. Exterior angles are formed with one side and by extending its adjacent side at the vertex. The exterior angle sum theorem states that the sum of all exterior angles of any polygon is 360 degrees.

To find the measure of a single exterior angle, we simply divide the measure of the sum of the exterior angles with the total number of sides in the polygon. The sum of interior angles is given by 180 (n – 2), where n is the number of sides. Since all interior angles in a regular polygon are equal, we can say that the measure of an exterior angle of a regular polygon with N sides is equal to 360oN.

In a regular polygon, the exterior angle can be found by dividing 4 right angles by the number of sides, which equals 4*90=360 degrees. In a regular hexagon, the exterior angle can be found by dividing the sum of the exterior angles, 360°, by the number of sides/angles of the hexagon. The exterior and interior angles are supplementary, so the exterior angle = 180 – 108 = 72.

In summary, the exterior angles of a polygon are formed when extending the sides of the polygon, and the sum of all exterior angles is equal to 360 degrees.