Exterior Angle of a Polygon
Angle formed by a side and an extension of an adjacent side. (3.5)
An exterior angle of a polygon is an angle that is formed by one side of the polygon and the extension of the adjacent side. For example, in the polygon shown below, angle BCD is an exterior angle formed by extending the side BC and forming an angle with side CD.
The size of an exterior angle is equal to the sum of the two interior angles that are adjacent to it. To see this, we can draw a line from the vertex of the exterior angle to the opposite vertex of the polygon, as shown below.
We can see that the line divides the polygon into two smaller triangles, each with one of the interior angles adjacent to the exterior angle. Since the interior angles of a triangle add up to 180 degrees, the sum of the two interior angles is 180 degrees. Therefore, the size of the exterior angle is equal to the sum of the two interior angles.
We can also use this formula to find the size of each exterior angle in a regular polygon. Since a regular polygon has equal interior angles, we can divide the sum of all the interior angles by the number of sides to get the measure of each interior angle. Then, using the formula above, we can find the size of each exterior angle.
In summary, an exterior angle of a polygon is formed by one side of the polygon and the extension of the adjacent side, and its size is equal to the sum of the two interior angles adjacent to it.
More Answers:
Parallel Lines: Key Characteristics And Real-Life ApplicationsMastering The Math Of Slope With The Ultimate Formula For Inclination And Steepness
Remote Interior Angles: Theorem & Calculation For Polygon Geometry