You are making necklaces for your friends. you have 72 blue beads and 42 red beads. each friend will receive an identical necklace, and all beads must be used. what is the greatest number of friends who can receive a necklace? explain your reasoning. how many of each color bead will each friend receive on the necklace? explain your reasoning.

The greatest number of friends who can receive a necklace is 6. The reason why is because 6 is the greatest common factor of 72 and 42.

Each friend will have 12 blue beads and 7 red beads. If you divide 6 (GCF) with both numbers you get 12 and 7.

Hope this helps :3

∠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.