Question

Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and bare supplementary ( 5 points)

Answer 1

Answer:

See proof below

Step-by-step explanation:

Two angles that are linear pair sums up to 180°

If angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, then;

1+a = 180....1

2+b= 180....2

Taking the sum of both equations

1+2+a+b = 360°... 3

Note that the sum of the adjacent angles will also be 180° since they also lie on the same straight line, hence;

1+2 = 180°...4.

Substitute 4 into 3

From 3;

1+2+a+b = 360°

(1+2)+(a+b) = 360°

180+(a+b) = 360

a+b = 360-180

a+b = 180

Since the sum of a and b is 180°, this shows that angles are supplementary since the sum of 2 supplementary angles is also 180°

Hence this shows that the consecutive interior angles a and bare supplementary.