Question 7
#7) What value of m makes the equation true?
3(8 – m) = 5m – 40

8

Step-by-step explanation:

3(8-m)=5m-40

you first distribute 3 through the parenthesis

24-3m=5m-40

Move the variable to the left and change sign

24-3m-5m=-40

now move the constant to the right

-3m-5m=-40-24

collect like terms

-8m=-40-24

-8m=-64

Divide both sides by -8 and negative divide negative number becomes positive

so m = 8

∠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.

i think it is 70

step-by-step explanation: