Lines g, h, and l are parallel and m< 2 = 129°.

what is m 12?

a.
51°

b.
61°

c.
129°

d.
151°

option:A  is correct.

Step-by-step explanation:

Since g,h and l are parallel lines and a line intersect these 3 lines making angles 1,2,....12.

By looking at the figure we could say that

∠2=∠6 since they are pair of corresponding angles.

Hence ∠6=129°

similarly ∠6=∠10 as they are also pair of corresponding angles.

Hence ∠10=129°

Now we know that ∠10+∠12=180° .

(since both the angles lie on a straight line)

129°+∠12=180°

∠12=180°-129°

∠12=51°

Hence option A is correct.(i.e. measure of ∠12 is 51°)

∠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.

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step-by-step explanation: