Brett has 100 feet of fence with which to make a rectangular cage for his dog. The area of the cage in square feet is given by the polynomial where w is the width of the cage in feet. What is the area of the cage if the width is 8 feet?

Area of rectangle cage = 336 feet²

Step-by-step explanation:

Given:

Wire required for fencing = 100 feet

Width of rectangular cage = 8 feet

Find:

Area of rectangle cage

Computation:

Wire required for fencing = perimeter of cage

Perimeter of rectangular cage = 100 feet

2[l + b] = 100 feet

l + 8 = 50 feet

Length of rectangular cage = 42 feet

Area of rectangle cage = Length x Width

Area of rectangle cage = 42 x 8

Area of rectangle cage = 336 feet²

∠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.