Understanding Exterior Angles in Polygons: The Exterior Angle Theorem Explained

Exterior Angles

Exterior angles are angles formed when a side of a polygon is extended

Exterior angles are angles formed when a side of a polygon is extended. More specifically, when you extend a side of a polygon, the angle formed between the extended side and the adjacent side inside the polygon is called the exterior angle.

To understand exterior angles better, let’s consider a triangle as an example. If we have a triangle with sides AB, BC, and AC, then we can extend one of the sides, let’s say side AB. The exterior angle would be the angle formed between the extended side AB and the side AC.

In general, the measure of an exterior angle of a polygon can be found by taking the difference between 180 degrees and the measure of the corresponding interior angle. This can be stated as the Exterior Angle Theorem: the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles.

Let’s illustrate this with an example. Consider a regular pentagon (a polygon with 5 sides of equal length). To find the measure of each exterior angle, we can start by finding the measure of the corresponding interior angle. Since the sum of the interior angles of any polygon is given by the formula (n-2) * 180°, where n is the number of sides, for a regular pentagon, the sum of the interior angles is (5-2) * 180° = 540°. Therefore, each interior angle of a regular pentagon measures 540° / 5 = 108°.

Now, let’s use the Exterior Angle Theorem to find the measure of each exterior angle. The exterior angle is equal to 180° minus the measure of the corresponding interior angle, so each exterior angle of a regular pentagon measures 180° – 108° = 72°.

In summary, exterior angles are formed when a side of a polygon is extended, and their measures can be found by taking the difference between 180° and the measure of the corresponding interior angle. The Exterior Angle Theorem is a useful tool for calculating the measures of exterior angles in polygons.

More Answers: