Question

Please Help!! What is the next step in the proof? Choose the most logical approach.

A.

Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7


Reason: Congruent Supplements Theorem


B.

Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180°


Reason: Linear Pair Theorem


C.

Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180°


Reason: definition of supplementary angles


D.

Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5


Reason: Vertical Angles Theorem

Answer 1

d

Explanation:

Answer 2

statement D is correct.

Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5

Reason: Vertical Angles Theorem

Explanation:

Given that

3 ≅ ∠7 and ∠4 ≅ ∠8

from statement 2 because they are corresponding angles.

∠8 ≅ ∠5

because its vertical angles

The vertical angles theorem is about angles that are opposite each other.

So,

∠4 ≅ ∠8 and ∠8 ≅ ∠5

which means

∠4 ≅ ∠5

Hence,

∠3 = ∠7

∠4 = ∠5

they are known as interior alternative angles.