Provide the missing statements and reasons for the following proof: Given: Line m is parallel to line n. Prove: ∠1 is supplementary to ∠2.
Given: Line
m
is parallel to line
n
.
Prove:
∠
1

is supplementary to

∠
2
.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

Learn more about supplementary angles on:

its a straight line parallel to the time axis