Question

Please help!

Answer 1

Answer:

Use the drop-down menus to complete the proof.

Given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the

✔ corresponding angles theorem

. Therefore, m∠1 = m ∠5 by the definition of congruent. We also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the

✔ linear pair postulate

. By the

✔ definition of supplementary angles

, m∠3 + m ∠1 = 180. Now we can substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary

Step-by-step explanation:

Answer 2

Answer:

1.Corresponding angles theorem

2.Linear postulate

3.By the definition of supplementary angles

Step-by-step explanation:

We are given that  

$w\parallel x$and y is a transversal.

We have to prove $\angle 3$ and $angle 5$ are supplementary

Proof:

1.Given that $w\parallel x$ and y is a transversal.

We know that $\angle 1\cong \angle 5$

Reason:Corresponding angles theorem

Therefore, $m\angle 1=m\angle 5$

by the definition of congruent.We also know that, by definition, angle 3 and angle 1 are a linear pair.

Therefore, they are supplementary by linear pair postulate

By the definition of supplementary angles

$m\angle 3+m\angle 1=180^{\circ}$

Now, we can substitute $m\angle 5=m\angle 1$

Then, we get

$\m\angle 3+m\angle 5=180^{\circ}$

Therefore, by the definition of supplementary angles,angle 3 and angle 5 are supplementary