A group of nine friends go to a baseball game. Each friend buys either a hamburger or hot dog at the game.
The group buys 6 hot dogs and 3 hamburgers for a total of $27.75.
• A hamburger costs $1.75 more than a hot dog.
What is the cost of a hamburger?
A
$2.50
B
$3.25
$3.75
$4.25

$4.25

Step-by-step explanation:

27.75 - 5.25 = 22.5

22.5/9 = 2.5

2.5 + 1.75 = 4.25

∠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.