Julian and marco are brothers who like to make bets about the outcomes of different contests between them. before the last bet, the ratio of the amount of julian's money to the amount of marco's money was 2: 3. marco lost the latest competition, and now the ratio of the amount of julian's money to the amount of marco's money is 4: 2. if marco had $180 before the last competition, how much does marco have now that he lost the bet?

100 dollars

Step-by-step explanation:

Let us first establish the fact that losing a bet means that one brother will lose part of his money to another brother, meaning that the sum of their money will remail the same.

Now, it is given that, before the last bet, Marco had $180 and that the ratio Julian: Marco was 2 : 3.

If we make a proportion, we will get;

x : $180 = 2 : 3

x = $120

So, before the last bet, Julian had $120, meaning that the sum of their money was $300.

After the last bet, sum remained the same, only the ratio changed (4:2).

That means that:

4x + 2x = $300

6x = $300

x = $50

So, Julian now has 4 • $50 = $200 and Marco has 2 • $50 = $100.

true

step-by-step explanation:

∠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.