A pentagon has actually 5 sides, and also can be 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 to 3 × 180° = 540°

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

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

The internal Angles that a Pentagon add up to 540°

## The general Rule

Each time we add a side (triangle come quadrilateral, square to pentagon, etc), us add one more 180° to the total:

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If that is a Regular Polygon (all sides room 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: How Much Is A 48 Star Flag Worth, 48 Star Flag ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general ascendancy is:

Sum of inner Angles = (n−2) × 180°

Each angle (of a continual Polygon) = (n−2) × 180° / n

Perhaps an example will help:

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

And for a consistent Decagon:

Each inner angle = 1440°/10 = 144°

Note: interior Angles room sometimes dubbed "Internal Angles"

internal Angles Exterior Angles degrees (Angle) 2D shapes Triangles quadrilateral Geometry Index