What is the measure of each exterior angle in a regular pentagon?

The measure of each exterior angle in a regular pentagon is 72 degrees.

In a regular pentagon, all sides and angles are equal. To find the measure of each exterior angle, you can use the formula for the exterior angles of any regular polygon. The sum of the exterior angles of any polygon is always 360 degrees. Since a pentagon has five sides, you divide 360 degrees by 5.

So, 360 degrees ÷ 5 = 72 degrees.

This means each exterior angle of a regular pentagon measures 72 degrees. Exterior angles are the angles formed between one side of the polygon and the extension of an adjacent side. In a regular pentagon, because all sides and angles are equal, each exterior angle will be the same.

Understanding this concept is useful because it helps you to analyse and solve various geometric problems involving regular polygons. For instance, knowing the measure of exterior angles can help you find the measure of interior angles, as the interior and exterior angles at each vertex of a polygon are supplementary (they add up to 180 degrees). Therefore, in a regular pentagon, each interior angle would be 180 degrees - 72 degrees = 108 degrees. This knowledge is fundamental in geometry and can be applied to more complex shapes and problems.