Triangles Contain 180°

Triangle with angles A,B,C

In a triangle, the three angles always add to 180°:

A + B + C = 180°

Try it yourself (drag the points):


We can use that fact to find a missing angle in a triangle:

Example: Find the Missing Angle "C"

Triangle Missing Angle

Start With:   A + B + C = 180°
     
Fill in what we know:   38° + 85° + C = 180°
     
Rearrange   C = 180° - 38° - 85°
     
Calculate:   C = 57°

Proof

This is a proof that the angles in a triangle equal 180°:

Proof the angles in a triangle add to 180

The top line (that touches the top of the triangle) is
running parallel to the base of the triangle.

So:

  • angles A are the same
  • angles B are the same

And you can easily see that A + C + B does a complete rotation from one side of the straight line to the other, or 180°