Angle properties of triangles

We already know that the angles in a triangle add up to 180°. Angles on a straight line also add up to 180°.

In the diagram, we see that:

a + b + c = 180° (angles in a triangle)

and

c + d = 180° (angles on a straight line).

If we rearrange both equations (subtract c from both sides), we get:

a + b = 180° - c and d = 180° - c.

Therefore, a + b and d must be the same (they are both equal to 180° - c):

a + b = d

Now look again at the diagram.

The exterior angle is equal to the sum of the two opposite interior angles.

This is true for any triangle.