A pentagon has actually 5 sides, and can be made indigenous three triangles, therefore you understand what ...

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

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

(Exercise: make sure each triangle here adds up to 180°, and also check the the pentagon"s interior angles include up to 540°)

The inner Angles of a Pentagon include up to 540°

The basic Rule

Each time we add a side (triangle come quadrilateral, quadrilateral to pentagon, etc), us add an additional 180° to the total:


ShapeSidesSum ofInterior AnglesShapeEach Angle
If that is a Regular Polygon (all sides space equal, all 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 ascendancy is:


Sum of inner Angles = (n−2) × 180°

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


Perhaps an instance will help:


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

*


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

And because that a continual Decagon:

Each internal angle = 1440°/10 = 144°


Note: inner Angles space sometimes referred to as "Internal Angles"


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