Question

State the missing reason in this flow proof

Answer 1

The complete flow proof is:

1. $\angle 5 = 40^o$ ---- Given
2. $\angle 2 = 140^o$ ---- Given
3. $\angle 5 + \angle 2 = 180^o$ ----- $\angle 5$ and $\angle 2$ are supplementary angles
4. $\angle 5 + \angle 2 = 180^o$ ----- $\angle 5$ and $\angle 2$ are same-side interior angles
5. $a ||b$ ----- Proved

We have:

$\angle 5 = 40^o$

$\angle 2 = 140^o$

The proof of $a ||b$ is as follows:

The first statement is:

$\angle 5 = 40^o$ ---- Given

The next statement is:

$\angle 2 = 140^o$ ---- Given

Supplementary angles add up to $180^o$.

So, the third statement is:

$\angle 5 + \angle 2 = 180^o$ ----- $\angle 5$ and $\angle 2$ are supplementary angles

Same side of interior angles add up to $180^o$.

So, the fourth statement is:

$\angle 5 + \angle 2 = 180^o$ ----- $\angle 5$ and $\angle 2$ are same-side interior angles

Because the angles are supplementary angles and also same-side interior angles, then it means that line a is parallel to line b

So, the last statement is:

$a ||b$ ----- Proved

Read more about proofs of parallel lines at:

brainly.com/question/18396272