A pentagon has actually 5 sides, and also can be made native three triangles, so you understand what ...

You are watching: How many degrees are in each interior angle of a regular pentagon?

... Its inner angles add up come 3 × 180° = 540°

And when it is regular (all angles the same), then each angle is 540° / 5 = 108°

(Exercise: make certain each triangle right here adds as much as 180°, and also check the the pentagon"s inner angles add up come 540°)

The inner Angles the a Pentagon include up come 540°

## The basic Rule

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If that 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: Middle School Math With Pizzazz Book A Th With Pizzazz Book A Pdf ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general rule is:

Sum of internal Angles = (n−2) × 180°

Each edge (of a continuous Polygon) = (n−2) × 180° / n

Perhaps an example will help:

### Example: What about a continual Decagon (10 sides) ? Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And for a regular Decagon:

Each inner angle = 1440°/10 = 144°

Note: inner Angles are sometimes called "Internal Angles"

interior Angles Exterior Angles degrees (Angle) 2D forms Triangles quadrilateral Geometry Index