## Two parallel lines cut by a curved line

Geometric formulae, word problems, theorems and proofs, etc.
1111
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### Two parallel lines cut by a curved line

How do you find x? It's not 38. Could it be 37? What is the use of the 75 angle?

nona.m.nona
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### Re: Two parallel lines cut by a curved line

How do you find x? It's not 38. Could it be 37? What is the use of the 75 angle?
Lacking information regarding "x", "38", "37", "the 75 [degree?] angle", or any other information regarding this exercise, I'm afraid there is no way to proceed. Kindly please enquire of your instructor regarding all the missing information. For instance, might s/he be able to provide some sort of image or instructions? Thank you.

1111
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### Re: Two parallel lines cut by a curved line

maggiemagnet
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### Re: Two parallel lines cut by a curved line

How do you find x? It's not 38. Could it be 37? What is the use of the 75 angle?
Okay; I'm going to guess that the exercise was actually something like this:
Given that lines L1 and L2 are parallel, that lines L3 and L4 meet at point "p" between lines L1 and L2, that the acute angle formed by lines L1 and L3 (and above line L1) measures 37 degrees, that the acute angle formed by lines L3 and L4 (and to the right of the intersection point p) measures 75 degrees, as displayed in the picture below:

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```picture: /L3 / /37* ----------------/--------- L1 / p /75* \ \ ----------------\--------- L2 \x \ \L4```
Based on this information find the measure, in degrees, of the angle labeled above as "x".
What did you try? How far did you get? After you drew a third line through p, parallel to the first two, what did you get from this?

Please show all of your thinking and attempts, so we can see where you're having trouble. Thank you!

1111
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### Re: Two parallel lines cut by a curved line

I drew dotted imaginary lines connecting L4 and L1 as well as L3 and L2, then used supplementary angle theorem to determine the missing angles by subtracting what were given by 180 and worked my way to x being 38. But that was not the answer.

maggiemagnet
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### Re: Two parallel lines cut by a curved line

I drew dotted imaginary lines connecting L4 and L1 as well as L3 and L2, then used supplementary angle theorem to determine the missing angles by subtracting what were given by 180 and worked my way to x being 38. But that was not the answer.
Okay; I'll need to see your work in order to check it. But, in the meantime, why not try drawing the line I suggested earlier?

1111
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### Re: Two parallel lines cut by a curved line

I drew a third line so the 75 split into 37 and 38, 38 being the bottom half. This means x is 38, which it isn't.

nona.m.nona
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### Re: Two parallel lines cut by a curved line

I drew a third line so the 75 split into 37 and 38, 38 being the bottom half. This means x is 38, which it isn't.
You still don't show your work, so we will have to guess. You likely started with something along these lines:

Code: Select all

```picture: \ /L3 \ / \ /37* -----------\----/--------- L1 \ /A _____________\/___________ L5 /\ B / \ -----------/----\--------- L2 / \x / \ / \L4```
The angle with measure 75 degrees is now split into two angles, being labeled as "A" and "B", with the measure of B, "m(B)", being equal to 75 - m(A). The new parallel line, as suggested by the previous helper, is labeled "L5".

It is assumed that you then applied the relevant theorem regarding corresponding angles with respect to the line L3 and the parallel lines L1 and L5, which gave you a value for m(A) of 37 degrees. You then plugged this value into the relation noted above to determine the value of m(B). It is guessed that you then applied the same theorem, this time with transversal L4 and parallel lines L5 and L2, to determine the value of m(x).j

On what logical basis have you decided that the measure of the angle labeled "x" is not 38 degrees? Please be complete, this time showing your work and reasoning. Thank you.