Please answer attached photo!

Step-by-step explanation:

The idea is to move the decimal to right after the repeating digit and then to right before it and subtract.

Let x = .46666

Then to move the decimal one place to right before the repeating digit, we multiply by ten which moves the decimal right after the 4 and right before the repeating 6:

10x = 4.666

Now we need to move it to right after the repeating digit, so we multiply by 100:

100x = 46.666 and subtract:

100x = 46.666

-10x =    4.666

99x = 42 so

x = 42/99

∠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.