A pentagon has actually 5 sides, and can it is in made native three triangles, so you know what ...

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

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

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

The interior Angles that a Pentagon add up to 540°

The basic Rule

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


ShapeSidesSum ofInterior AnglesShapeEach Angle
If the is a Regular Polygon (all sides space equal, every angles space 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 dominion is:


Sum of internal Angles = (n−2) × 180°

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


Perhaps an example will help:


Example: What about a constant Decagon (10 sides) ?

\"*\"


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

And because that a constant Decagon:

Each internal angle = 1440°/10 = 144°


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


interior Angles Exterior Angles degrees (Angle) 2D forms Triangles quadrilaterals Geometry Index