Revised: How to solve an exterior angle when you only know the interior angle and there are two liparallel lines with a transversal?

I changed the picture to a one drawn with MS paint to comply with copyright rules.

Need to learn how to solve for the red angle.

Can some one explain to me the therom used to solve this problem?

I'm more interested in understanding how to solve than I am in the answer. My limited knowledge of solving these problem requires me to know one more inside angle.


Thanks.
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jasgotAsked:
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ozoCommented:
Is there any restriction on where M can be along AB?
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jasgotAuthor Commented:
No. the only known values are the 50 degree angle and the parallel lines.
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ozoCommented:
Depending on where M is (inferring from the picture that it is to the left of G)
MHC could be anywhere between 0 and 180-50

Given parallel lines, we know that MHC=GMH, so If we were given something like a relationship between MHG and GMH, then perhaps we could say more.
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jasgotAuthor Commented:
I know that. But I need to know to solve it.
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ozoCommented:
Without more information, the angle MHC cannot be determined.

You might measure it off the diagram, but that's not how these diagrams are usually meant to work, since the diagram could have been drawn differently.

That the diagram could have been drawn differently  with a different MHC angle, further indicates that MHC is undetermined.
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jasgotAuthor Commented:
After re-reading the problem. I realize I did have more information. MH BISECTS CHG. How I missed this before I don't know. But at least now I know am not an idiot. I knew there had to be more information, and it was there all along. Thanks for spending your Sunday afternoon thinking about me and my dilemma. Cheers to you for your time.
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ozoCommented:
If you know CHG, you know the what an angle bisecting CHG must be.
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jasgotAuthor Commented:
Indeed!
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