A pentagon has 5 sides, and can be made native three triangles, for this reason you recognize what ...

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

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

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

The interior Angles of a Pentagon add up come 540°

## The general Rule

ShapeSidesSum ofInterior AnglesShapeEach Angle
 If it is a Regular Polygon (all sides room equal, every 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: The Meaning Of Cherry Blossom Tree Tattoo Designs & Ideas To Try In 2021 ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general rule is:

Sum of inner Angles = (n−2) × 180°

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

Perhaps an example will help:

### Example: What about a regular Decagon (10 sides) ?

Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°

And for a continuous Decagon:

Each inner angle = 1440°/10 = 144°

Note: internal Angles are sometimes referred to as "Internal Angles"

inner Angles Exterior Angles levels (Angle) 2D shapes Triangles quadrilateral Geometry Index