A pentagon has 5 sides, and also can be made indigenous three triangles, for this reason you know what ...

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

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

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

The interior Angles that a Pentagon add up come 540°

## The general Rule

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

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If the 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: When Going 70 Mph It Takes How Many Feet To Stop Including Reaction Time ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general dominance is:

Sum of internal Angles = (n−2) × 180°

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

Perhaps an example will help:

### Example: What around a regular Decagon (10 sides) ? Sum of interior Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And for a consistent Decagon:

Each interior angle = 1440°/10 = 144°

Note: internal Angles are sometimes called "Internal Angles"

inner Angles Exterior Angles levels (Angle) 2D forms Triangles square Geometry Index