Exterior angles Chapter 5 (p. 225)
Angles that form linear pairs with the interior angles of a polygon
Exterior angles are angles formed outside of a polygon when one side of the polygon is extended. The exterior angle is the angle between the extended side and the adjacent side of the polygon. The sum of all the exterior angles of a polygon is always equal to 360 degrees.
To find the measure of an exterior angle of a regular polygon, we can use the formula:
Exterior angle = 360 degrees ÷ number of sides
For example, if we have a regular hexagon (a polygon with six sides), the measure of each exterior angle would be:
Exterior angle = 360 degrees ÷ 6 sides = 60 degrees
We can also find the measure of an exterior angle of any polygon by dividing the sum of all the exterior angles by the number of sides.
For example, if we have a polygon with 8 sides, we know that the sum of all the exterior angles is 360 degrees. Therefore, each exterior angle would measure:
Exterior angle = 360 degrees ÷ 8 sides = 45 degrees
Knowing the measure of exterior angles can be useful in solving problems involving polygons, such as finding missing angles or lengths of sides.
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