How can it be proved that the sum of angles of a triangle equal 180 degrees.

Let ABC be a triangle.

Exend
AC to X from C.

Draw a line CD frm C which is || to
AB.

Now AB || CD and BC is a
transvalal.

Therefore angle ABC = angle BCD being alternate
angle.

Therefore angle CAB = angle DCX being corresponding
angles.

Therefore angle CAB + angle ABC +angle ACB = Angle
ACB+Angle ABD+Angle DCX. The right side is the sum of angle on the straight line, which
is 180 degree.

This proves that the sum of
the angles of a triangle is 180 degrees.