Can someone ? i don’t understand this.

PS = 28 units.

Step-by-step explanation:

See the attached diagram.

This is a figure of rectangle with length (3y + 3) and width 4y.

Now, the perimeter of the rectangle is 2[(3y + 3) + 4y] = 2(7y + 3)

The perimeter of the rectangle is given to be 104 units.

So, 2(7y + 3) = 104

⇒ 7y + 3 = 52

⇒ 7y = 49

⇒ y = 7

Therefore, PS = 4y = 4(7) = 28 units. (Answer)

the circle one

∠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.