A pentagon has actually 5 sides, and can it is in made native three triangles, therefore you recognize what ...

You are watching: What is the measure of each interior angle of a regular pentagon?

... Its interior angles include up come 3 × 180° = 540°

And as soon as it is regular (all angle the same), then each edge is 540° / 5 = 108°

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

The internal Angles of a Pentagon include up come 540°

## The general Rule

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If it is a Regular Polygon (all sides room equal, all angles space 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 Does The Name Traci Mean ? What Does Traci Mean ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general ascendancy is:

Sum of interior Angles = (n−2) × 180°

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

Perhaps an example will help:

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

And for a consistent Decagon:

Each internal angle = 1440°/10 = 144°

Note: inner Angles room sometimes called "Internal Angles"

interior Angles Exterior Angles degrees (Angle) 2D shapes Triangles square Geometry Index