A pentagon has 5 sides, and can be made from three triangles, so you know what ...
You are watching: What is the measure of an interior angle of a regular pentagon?
... its interior angles add up to 3 × 180° = 540°
And when it is regular (all angles the same), then each angle is 540° / 5 = 108°
(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon"s interior angles add up to 540°)
The Interior Angles of a Pentagon add up to 540°
The General Rule
Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:
| If it is a Regular Polygon (all sides are equal, all angles are equal) | ||||
| Triangle | 3 | 180° |  | 60° |
| Quadrilateral | 4 | 360° |  | 90° |
| Pentagon | 5 | 540° |  | 108° |
| Hexagon | 6 | 720° |  | 120° |
| Heptagon (or Septagon) | 7 | 900° |  | 128.57...° |
| Octagon | 8 | 1080° |  | 135° |
| Nonagon | 9 | 1260° |  | 140° |
| ... | ... | .. | ... See more: What Is The Longest Street In The United States ? History Of Colfax Avenue | ... |
| Any Polygon | n | (n−2) × 180° |  | (n−2) × 180° / n |
So the general rule is:
Sum of Interior Angles = (n−2) × 180°
Each Angle (of a Regular Polygon) = (n−2) × 180° / n
Perhaps an example will help:
Example: What about a Regular Decagon (10 sides) ?
Sum of Interior Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°
And for a Regular Decagon:
Each interior angle = 1440°/10 = 144°
Note: Interior Angles are sometimes called "Internal Angles"
Interior Angles Exterior Angles Degrees (Angle) 2D Shapes Triangles Quadrilaterals Geometry Index