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)
Triangle3180°
*
60°
Quadrilateral4360°
*
90°
Pentagon5540°
*
108°
Hexagon6720°
*
120°
Heptagon (or Septagon)7900°
*
128.57...°
Octagon81080°
*
135°
Nonagon91260°
*
140°
...........

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...
Any Polygonn(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