The sum of three consecutive number odd integers is 18 less than five times the middle number find the three integers

1st number = x

2nd number = x+2

3rd number = x+4

x + x+2 +x+4 = 3x+6

3x+6 = 5(x+2)-18

3x+6 = 5x+10-18

3x+6 = 5x-8

3x+14 =5x

14 = 2x

x = 14/2 = 7

 1st number = 7

 2nd number = 7+2 = 9

3rd number = 7+4 = 11

∠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.