Dan has a board that is 8 3/4 feet long. He cuts off 4 5/6 feet and says he has 4 1/12 feet left. Which of the following explains whether Dan is correct?

A.

Yes, Dan is correct because 8 3/4 – 4 5/6 = 4 1/12.
B.

No, Dan is not correct because 8 3/4 – 4 5/6 = 3 1/4.
C.

No, Dan is not correct because 8 3/4 – 4 5/6 = 3 11/12.
D.

No, Dan is not correct because 8 3/4 – 4 5/6 = 4 3/4.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation: