Triangles Contain 180 Degrees - Math Is Fun

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Triangles Contain 180°

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

A + B + C = 180°

Try it yourself (drag the points):

geometry/images/triangle.js?mode=angles

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

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°:

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

Notice that:

And you can see that A + C + B rotates from one side of the straight line to the other, or a full 180°