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State the missing reasons in this flow proof.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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a-e
any one on?

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Other answers:

ty
wait do you mean the statements? like angleABC because the reasons are already there
not sure thats why I'm confused
I'm don't know what they're asking for :S sorry
k
is this you the one needed help for?
yes
got it thanks
A)∠5 is an acute angle (40º) B) ∠2 is an obtuse angle (140º) C) ∠2 + ∠5 = 180° forms a supplementary angle. therefore, forms a straight line D) If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary. E) If a transversal intersects two lines and the interior angles on the same side of the transversal are supplementary, then the lines are parallel.
Not good at this, never learned it.
this is a little confusing as I compose it, but I am sure it somewhat makes sense: ∠2 is congruent to ∠1 since ∠2 and ∠5 forms a straight line or a supplementary angles (180º) then ∠4 must be congruent to ∠1 and since ∠1 is congruent to ∠2 then ∠1 and ∠5 must also be supplementary angles, which proves that line a and b are parallel
a proof starts with whats 'Given' so we can simply put the reason 'Given' for a and b.
similarly we wil be good if we just put fill the blanks c,d, and e wid approproate reasons i guess
rephrasing: A) given ∠5 in line b is an acute angle (40º) B) another given ∠2 in line a is an obtuse angle (140º) you are right about filling out the blanks, but I am not sure if the sentences D and E are even appropriate to state
thanks for the guidance, @ganeshie8
:) c, your reason is good : 'supplementary angles add up to 180' d, we can simply fill wid : ' by Definition of same-side interior angles' e, we can fill wid : 'by Converse of same-side interior angles theorem'

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