A regular pentagon is a polygon with five equal sides and five equal angles. To find the measure of each interior angle, we can use the formula for calculating the interior angles of any polygon:
Interior Angle = (n – 2) × 180° / n
In this formula, n represents the number of sides in the polygon. Since a pentagon has five sides, we set n = 5:
- Calculate the number of triangles that can be formed by drawing diagonals from one vertex: n – 2 = 5 – 2 = 3
- Multiply the number of triangles by 180°: 3 × 180° = 540°
- Now, divide the total sum of the interior angles by the number of angles (which is also the number of sides):
540° / 5 = 108°
Thus, each interior angle in a regular pentagon measures 108 degrees.
This means that in a regular pentagon, all five interior angles are equal to 108°, creating a perfectly symmetrical shape that is both aesthetically pleasing and geometrically sound.