Angles of Polygons

Interior and Exterior Angles

Exterior Angles of a Polygon
Remember, a polygon is any shape that has 3 or more straight sides (no curves).

Click on the hexagon above to see that:

The exterior angles of any polygon add up to 360°

Interior Angles

90° + 60° + 30° = 180°	80° + 70° + 30° = 180°
It works for this triangle!	Let's tilt a line by 10° ... It still works, because one angle went up by 10°, but the other went down by 10°

The Interior Angles of a Triangle add up to 180° 

Because there are Two Triangles in a Square

The interior angles in this triangle add up to 180° (90°+45°+45°=180°)

... and for this square they add up to 360° ... because the square can be made from two triangles!

Because a pentagon has three triangles, the sum of the interior angles add up to 3x180° = 540°






 In general:

The sum of the interior angles of a polygon that has n sides, is:

(n-2) x 180°

Triangles in a circle:

The triangle drawn on the diameter of a circle is always 

a right angled triangle