Interior Angles of Polygons

Interior Angles of Polygons

Show Ads
Hide Ads
About Ads

2D Shapes

Regular Polygons

A polygon is a plane (2D) shape with straight sides.
To be a regular polygon all the sides and angles must be the
same:

2d triangle
Triangle – 3 Sides
2d square
Square – 4 Sides
2d pentagon
Pentagon – 5 Sides
2d hexagon
Hexagon – 6 sides
2d heptagon
Heptagon – 7 Sides
2d octagon
Octagon – 8 Sides
2d nonagon
Nonagon – 9 Sides
2d decagon
Decagon – 10 Sides
More …

 

Other Common Polygons

2d quadrilateral
Quadrilateral
Any 4 sided 2D shape
2d rectangle
Rectangle – 4 Sides
All right angles
And many more!

 

Curved Shapes

These 2D shapes have curves, so are not polygons:

2d circle
Circle
2d ellipse
Ellipse
And many more!

 

 
Polygons (more detail) Geometry Index

Search :: Index :: About :: Contact :: Contribute :: Cite This Page :: Privacy

Copyright © 2015 MathsIsFun.com



ClipArt ETC

7-sided Polygon

7-sided Polygon

Small

320×312

7-sided Polygon

Medium

640×624

7-sided Polygon

Large

1024×998

Download TIFF

Original

3077×3000 | (230.0 KB)

Download EPS

Vector

343.4 KB

Description

Polygon consisting of 7 sides

Keywords

7 sides , 7-sided , closed figure , faces , Geometric , geometry , polygon , septagon , seven sides

Galleries

Heptagons

Source:

Florida Center for Instructional Technology Clipart ETC (Tampa, FL: University of South Florida, 2009)

Math is Fun

Show Ads
Hide Ads
About Ads

Interior Angles of Polygons

An Interior Angle is an angle inside a shape

interior exterior angles

Another example:

interior exterior angles

Triangles

The Interior Angles of a Triangle add up to 180°

Let’s try a triangle:
interior angles triangle 90 60 30
90° + 60° + 30° = 180°

It works for this triangle

Now tilt a line by 10°:

interior angles triangle 80 70 30
80° + 70° + 30° = 180°

It still works!
One angle went up by 10°,
and the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

Let’s try a square:
interior angles square 90 90 90 90
90° + 90° + 90° + 90° = 360°

A Square adds up to 360°

Now tilt a line by 10°:
interior angles 100 90 90 80
80° + 100° + 90° + 90° = 360°

It still adds up to 360°

The Interior Angles of a Quadrilateral add up to 360°

Because there are 2 triangles in a square …

interior angles 90 (45,45) 90 (45,45)

The interior angles in a triangle add up to 180°

… and for the square they add up to 360°

… because the square can be made from two triangles!

Pentagon

interior angles pentagon

A pentagon has 5 sides, and can be made from three triangles, so you know what …

… its interior angles add up to 3 × 180° = 540°

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

(Exercise: make sure each triangle here adds up to 180°, and check that the pentagon’s interior angles add up to 540°)

The Interior Angles of a Pentagon add up to 540°

The General Rule

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

   If it is a Regular Polygon (all sides are equal, all angles are equal)
ShapeSidesSum of
Interior Angles
ShapeEach Angle
Triangle 3180°regular triangle60°
Quadrilateral 4360°regular quadrilateral90°
Pentagon 5540°pentagon regular108°
Hexagon 6720°hexagon regular120°
Heptagon (or Septagon)7900°heptagon refular128.57…°
Octagon81080°octagon regular135°
Nonagon91260°nonagon regular140°
..
Any Polygonn(n-2) × 180°regular n gon(n-2) × 180° / n

So the general rule is:

Sum of Interior Angles = (n-2) × 180°

Each Angle (of a Regular Polygon) = (n-2) × 180° / n

Perhaps an example will help:

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

regular decagon

Sum of Interior Angles = (n-2) × 180°
 = (10-2)×180° = 8×180° = 1440°

And it is a Regular Decagon so:

Each interior angle = 1440°/10 = 144°

 

Note: Interior Angles are sometimes called "Internal Angles"

 

Interior Angles Exterior Angles Degrees (Angle) 2D Shapes Triangles Quadrilaterals Geometry Index

Copyright © 2016 MathsIsFun.com