A pentagon has actually 5 sides, and also can it is in made from three triangles, for this reason you recognize what ...

You are watching: Angles of a quadrilateral add up to

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

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

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

The inner Angles that a Pentagon add up to 540°

The basic Rule

Each time we add a next (triangle to quadrilateral, square to pentagon, etc), us add another 180° to the total:


ShapeSidesSum ofInterior AnglesShapeEach Angle
If that is a Regular Polygon (all sides space equal, all angles are equal)
Triangle3180°
\"*\"
60°
Quadrilateral4360°
\"*\"
90°
Pentagon5540°
\"*\"
108°
Hexagon6720°
\"*\"
120°
Heptagon (or Septagon)7900°
\"*\"
128.57...°
Octagon81080°
\"*\"
135°
Nonagon91260°
\"*\"
140°
...........

See more: Classic Cars That Start With The Letter F Ull List, List Of Current Automobile Marques

...
Any Polygonn(n−2) × 180°
\"*\"
(n−2) × 180° / n

So the general preeminence is:


Sum of inner Angles = (n−2) × 180°

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


Perhaps an instance will help:


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

\"*\"


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

And for a regular Decagon:

Each inner angle = 1440°/10 = 144°


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


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