Angles in Polygons

Shape

Picture

Number of Sides

Interior Angle

Sum of Interior Angles

Exterior Angle

Triangle

3

60

180

120

Square

4

90

360

90

Pentagon

5

108

540

72

Hexagon

6

120

720

60

Octagon

8

135

1080

45

n- agon

To see why the angles in a triangle add tonotice that a triangle has three sides so n=1 and the angles add to 180, a square can be cut into two triangles, each with internal angles 180, so all the internal angles of both triangles sum to 360. Consider the pentagon below. It is cut into three triangle, each with internal angles that sum to 360, so the internal angles of a pentagon sum to 3*180 =540.

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