A survey asked 816 college freshman‘s whether they had been to a movie or eaten in a restaurant during the past week. The following information was obtained 390 freshman‘s have been to neither a movie nor a restaurant, and 263 had been to a movie. If 87 of those who have been to a movie had not been to a restaurant, how many of the surveyed freshman‘s have been to the following? (A) Both Movies and a Restaurant

(B) A movie or a restaurant

(C) a restaurant

(D) a restaurant but not a movie

∠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.

the answer i believe is 27 units.

step-by-step explanation:

there still no table