2.2 Sum of the angles of a triangle
It can be proven easily that the sum of the three angles of a D is 1800
D ABC in figure 2.2 is a triangle with line l parallel to seg. BC and passing through A. seg. AB is a transversal on two parallel lines seg. PQ and seg.BC. Hence m Ð PAB and m ÐABC are equal as they are alternate interior angles. Similarly m Ð QAC = m Ð ACB.
Now Ð PAQ = m Ð PAB + m Ð BAC + m Ð CAQ
i.e. 1800 = m Ð ABC + m Ð BAC + m Ð ACB
m Ð PAQ = 1800 because it is a straight line. Thus the sum, of the measures of the three angles, of any triangle, is 1800.