A400 foot long fence has posts that are placed 8 feet on center. that is the distance between the centers of two adjacent posts is 8 feet. if the fence begins and ends with a post, how many posts are needed for the fence?

The total length of the fence in feet = 400 feet

Posts are required at a distance of 8 feet

Total number of posts required = 400/8 = 50 posts

The 50 posts will include the post at the end since the last post will be placed at the 400 feet position which would mark the end of the fence.

Additionally, one more post will be required at the beginning since the first post will be placed at 8 feet from the start.

So total number of posts = 50 + 1 = 51 posts

Total number of posts required for the fence if it begins and ends with a post = 51 posts

∠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.

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.