If a+b+b =24 and b-a =4 what is a?

a = 5 1/3

Step-by-step explanation:

a+b+b = 24

a + 2b = 24

b-a =4

a = b - 4

b - 4 + 2b = 24

3b = 24 + 4

b =28/3

substitute this in a = b - 4

a = 28/3 - 4

a = 28/3 - 12/3

a = 16/3

a = 5 1/3

∠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.

1. perpendicular

2. parallel

3. perpendicular