Four consecutive numbers have a sum of –30. What number is x?

- 9

Step-by-step explanation:

Let the four consecutive numbers be x, x + 1,

x + 2 and x + 3.

x + x + 1 + x + 2 + x + 3 = - 30

x + x + x + x + 1 + 2 + 3 = - 30

4x + 6 = - 30

4x = - 30 - 6

4x = - 36

x = - 36 / 4

x = - 9

∠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.