Afamily is building a rectangular fountain in the backyard. the yard is rectangular and measures 8x by 9x. the fountain is going to measure 2x by 5x. once the fountain is built, what will be the area of the remaining yard?

Area of rectangle(A) is given by:

where,

l is the length and w is the width of the rectangle

As per the statement:

a family is building a rectangular fountain in the backyard. the yard is rectangular and measures 8x by 9x

⇒

It is also given that:

The fountain is going to measure 2x by 5x.

We have to find the area of the remaining yard.

⇒ [Combine like term]

Therefore, the area of the remaining yard is,

step-by-step explanation:

∠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.