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Triangles - computing angles

Dear experts I need help on the attached geometric (Triangle) Figure

Find the value of X from the adjoining diagram:

Kindly let me know if any theorem is available which explains the geometric properties of this triangle.
Ang  =Angle
IMG_3925.JPG
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Excellearner
Asked:
Excellearner
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1 Solution
 
Rich WeisslerProfessional Troublemaker^h^h^h^h^hshooterCommented:
You can solve this two ways.  First by drawing a line to split the 60 degree angle, and solve it materially like your previous question... and that would solve it using triangles.

Alternately, you can recognize that the interior angles of a quadrilateral sum to 360 degrees, and again that the angles of a circle sum to 360 degrees.

So you already know two of the interior angles, and you know one others can be solves by (360-132)... and that the sum of those three plus 'x' = 360.

Hopefully that gives you enough to solve.  (And I'd suggest solving it both way to check your answer.  :-) )
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ExcellearnerAuthor Commented:
Hi phoffric, thank you for your feedback. I see it as positive.

I we I'll send for of the questions I have posted my workings n show when am stuck.

I am happy to receive views of any type as every view only helps me get better.

Thank you
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ExcellearnerAuthor Commented:
Few typos errors as I am not used to mobile gadgets
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ExcellearnerAuthor Commented:
Dear experts,

I have worked the problems ‘myself’ without any help from anyone.
Please accept my apologies that I had to seek your help on some simple problems. Originally when I first tried to solve these questions, I panicked when I could not work the angles. It was then I posted the questions in Experts Exchange.
Today morning I woke up early 4 am (India time) and I sat down to work the angles myself. Surprisingly, I could work the angles.
I am attaching my workings for your review. All writings in ‘red’ ink is to show how I improvised the triangle to help resolve the angle.
Kindly let me know if you think if I have not understood correctly.
Also I will appreciate if someone can provide me a link where there are more tough diagrams shown which will enhance my understanding.
I am preparing for GMAT and I am self-learning Math topics. My subjects in college or A levels (Class Xi and XII) did not include Math and hence this struggle.
I have seen a few posts which are very encouraging and considerate in its response while considering that my ask in this forum may be too much (and not in line with the EE Policy). Having said that I have taken note of all the responses.

Thank you
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Rich WeisslerProfessional Troublemaker^h^h^h^h^hshooterCommented:
Excellent job on that problem.  I can find no mistake.

If you're studying the math for the GMAT, have you already looked at Khan Academy's GMAT section?  There's also a general 'Triangles' section, quite a bit when you get into the Trigonometry. and the misc section has a lot of triangle problems worked for the California Standards test.
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ExcellearnerAuthor Commented:
Thank you Rich for your support.
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