Miguel has 225 base ball cards. he plans to keep 75 cards and give the rest to his friends.

20) can miguel give an equal number of cards to 6 friends? explain.

21) can miguel give an equal number of cards to 4 friends? explain.

e. number sense:

**a number is divided by 2, and the remainder is 1. the same number is divided by 4, and the remainder is 3.

22) find the smallest such number.

23) find the next larger number.

20: Yes, because 125-75=150. If you divide 150 by 6, you would get 25.

21: No, because 125-75=150. If you divide 150 by 4, you would get 37.5.

*22: 1

*23: 5

*Explanation for both 22 and 23: If the number was 15, then 15 divided 2 would be 7 remainder 1. If 15 was divided by 4, it would be 3 remainder 3.

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

∠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.