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Interior Angles of Polygons

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An Interior Angle is an angle inside a shape

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

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Polygon Interior Angles – Math Open Reference

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Polygon Interior Angles – Math Open Reference

Try this
Adjust the polygon below by dragging any orange dot. Click on “make regular” and repeat.
Note the behavior of the interior angles and their sum.

The interior angles of a polygon are those angles at each
vertex that are on the inside of the polygon.
There is one per vertex. So for a polygon with N sides, there are N
vertices and N interior angles.

For a regular polygon,
by definition, all the interior angles are the same. In the figure above, Click on “make regular” then
change the number of sides and resize the polygon by dragging any vertex. Notice that for any given number of sides,
all the interior angles are the same.

For an irregular polygon,
each angle may be different. Click on “make irregular” and observe what happens
when you change the number of sides, and drag

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