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

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

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

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

The interior Angles of a Pentagon add up come 540°

## The basic Rule

Each time we add a side (triangle to quadrilateral, square to pentagon, etc), we add another 180° come 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: Who Is How Much Is Howard Hewett Worth 2021, Howard Hewett ... Any Polygon n (n−2) × 180° (n−2) × 180° / n

So the general preeminence is:

Sum of interior Angles = (n−2) × 180°

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

Perhaps an instance will help:

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

And because that a consistent Decagon:

Each inner angle = 1440°/10 = 144°

Note: internal Angles space sometimes called "Internal Angles"

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