Triangle angle sum theorem
The sum of the degree measures of the angles of a triangle is 180º.

aº + bº + cº = 180º

Proof:
In the following figure, line l has been drawn parallel to side AC of the triangle and through one of its vertices (B)

Since l||AC, alternate interior angles are equal in measure:

m<1 = m<4 and m<3 = m<5

The sum of the degree measures of the angles formed at vertex B is 180º:

m<4 + m<2 + m<5=180º

We may therefore substitute in the above equation m<1 for m<4 and m<3 for m<5:

m<1 + m<2 + m<3 = 180º