Understanding the Exterior Angle Theorem | Explained with Examples and Equations

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In geometry, the exterior angle of a polygon refers to the angle formed by one side of a polygon and the extension of the adjacent side

In geometry, the exterior angle of a polygon refers to the angle formed by one side of a polygon and the extension of the adjacent side.

To visualize this, imagine standing outside a polygon and looking at one of its vertices. The exterior angle is the angle you would see if you extended one of the sides of the polygon from that vertex.

The measure of an exterior angle can be determined using two concepts:

1. Sum of Exterior Angles: For any polygon, the sum of all its exterior angles is always 360 degrees. This means that if you were to measure all the exterior angles of a polygon and add them together, the result will be 360 degrees.

2. Exterior Angle Theorem: This theorem states that the measure of an exterior angle of a polygon is equal to the sum of the measures of the two non-adjacent interior angles. In other words, if you know the measure of two interior angles of a polygon, you can find the measure of the corresponding exterior angle by adding those two measures.

The exterior angle theorem can be represented by the equation:

Exterior Angle = Interior Angle 1 + Interior Angle 2

where Interior Angle 1 and Interior Angle 2 are the non-adjacent interior angles to the exterior angle.

It is important to note that the exterior angle theorem holds true for all convex polygons (polygons with all interior angles less than 180 degrees). For concave polygons (polygons with at least one interior angle greater than 180 degrees), the exterior angle may have a different measure or even be non-existent.

To find the measure of a specific exterior angle in a polygon, you need to know the measures of the two interior angles adjacent to it. Once you have those measures, you can simply apply the exterior angle theorem to find the measure of the exterior angle.

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