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

ShapeSidesSum ofInterior AnglesShapeEach Angle
 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