The histogram below shows information about the number of hamburgers students ate in a month:

A histogram is titled Hamburgers Eaten Monthly, the horizontal axis is labeled Hamburgers, and the vertical axis is labeled Students. The range on the horizontal axis is 0 to 4, 5 to 9, and 10 to 14. The values on the vertical axis are from 0 to 10 at intervals of 1. The first bin goes to 8, the second bin to 3, the third bin to 2.

Which information is provided in the histogram?

The mean number of hamburgers eaten

The median number of hamburgers eaten

The number of students who ate 5 hamburgers or fewer

The number of students who ate 10 hamburgers or more

∠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.

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5