PLEASE HELP THIS IS TIMED A gumball machine had 78 gumballs. Each person who put a coin into the machine gets 3 gumballs. After a certain number of people got gumballs, there were 54 gumballs remaining. Estimate how many people got gumballs out of the machine.

8 people got gumballs out of the machine.

Step-by-step explanation:

Given that:

Number of gumballs in machine = 78

Number of gumballs on each coin = 3

Number of gumballs left = 54

Let,

x be the number of people who put coin

Gumballs left = Total gumballs - 3*Number of people

54 = 78 - 3x

3x = 78 - 54

3x = 24

Dividing both sides by 3

Hence,

8 people got gumballs out of the machine.

∠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.