Sandy is working with a carpenter to frame a house. they are using 8-foot-long boards, but each board must be cut to be 94.6 inches long. how much is cut off each board? (1 foot = 12 inches)

Step-by-step explanation:

Given : The length of each board = 8 feet

We know that 1 feet = 12 inches.

Then, the length of each board =

Also, the each board must be cut to be 94.6 inches long.

Then, the length is cut off from each board =

Hence, of length is cut off each board .

∠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.