Finding The Polygon With The Exterior Angle Theorem?

The Exterior Angle Theorem is a mathematical formula that states that the measure of an exterior angle in a polygon is equal to the sum of two remote interior angles. It is used to find the exterior angles of a regular polygon with n sides, which are formed by extending one side of the polygon and between the extension and adjacent side.

The Exterior Angle Sum Theorem states that the exterior angles of any polygon are equal to the sum of two remote interior angles. The Exterior Angle Theorem is a crucial concept in geometry, as it states that the sum of all the exterior angles in a polygon is equal to 360°.

To find the exterior angles of a polygon, use the formula 360°/Number of sides of the polygon. For example, if there are 9 sides in the polygon, each exterior angle is equal to 360°/9, or 40°. The formula to calculate the measure of an exterior angle is: exterior angle of polygon = 360° ÷ number of sides = 360°/n.

For each interior angle of a regular polygon with n sides, the formula is: exterior angle measure = 360°/n. The sum of the measures of the exterior angles is the difference between the sum of measures of the linear pairs and the sum of measures of the interior angles. In a regular polygon with N sides, the measure of an exterior angle is equal to 360^o/N.