What Is The Plygon Exterior Angle Theorem?

A triangle has three interior angles and six exterior angles, which are the angles between a side of a triangle and an extension of an adjacent side. The sum of any polygon’s exterior three angles is always 360°. The exterior angle theorem states that when a triangle’s side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.

The exterior angles of a polygon are formed with its one side and by extending its adjacent side at the vertex. The sum of the exterior angles of any polygon is equal to 360 degrees. To calculate the sum of exterior angles for a polygon, one at each vertex, use the formula 360°/Number of sides of the polygon. If there are nine sides in the polygon, then each exterior angle is equal to the sum of the measures of the linear pairs and the sum of measures of the interior angles.

The size of one exterior angle is determined by adding up the Interior Angle and Exterior Angle. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides. Symmetry is another important aspect of the exterior angle theorem, as all exterior angles are equal.

In conclusion, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. This knowledge can be used to solve problems and prepare for exams such as Edexcel, AQA, and OCR GCSE.