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Step-by-step explanation:

Since the integers are consecutive,

let the smaller one be x

then the larger will be x+1

Now their sum is -15

x+x+1=-15

2x=-15-1

2x=-16

x=-8

Therefore the smaller is -8 and the larger is -7

Now when one is added to the smaller integer it becomes -8+1=-7

If 2 is subtracted from the larger one it becomes -7-2=-9

their product therefore becomes -9×-7=63

a² + b²= c²

24² + 7² = c²

c= 25

∠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.