A pentagon has actually 5 sides, and also can it is in made from three triangles, for this reason you recognize what ...

... Its interior angles add up to 3 × 180° = 540°

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

(Exercise: make certain each triangle here adds approximately 180°, and check that the pentagon\"s internal angles add up come 540°)

The inner Angles that a Pentagon add up to 540°

## The basic Rule

Each time we add a next (triangle to quadrilateral, square to pentagon, etc), us add another 180° to the total:

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If that is a Regular Polygon (all sides space 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: Classic Cars That Start With The Letter F Ull List, List Of Current Automobile Marques ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general preeminence is:

Sum of inner Angles = (n−2) × 180°

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

Perhaps an instance will help:

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

And for a regular Decagon:

Each inner angle = 1440°/10 = 144°

Note: interior Angles room sometimes dubbed \"Internal Angles\"

inner Angles Exterior Angles degrees (Angle) 2D shapes Triangles quadrilaterals Geometry Index