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Triangles - Calculating 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
d-degree
IMG_3922.JPG
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Excellearner
Asked:
Excellearner
2 Solutions
 
ste5anSenior DeveloperCommented:
Sums of angles in one triangle = 180°.
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d-glitchCommented:
Way too much help for a homework problem where the author is so disengaged.
But that is just my opinion.
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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 response.

Thank you
IMG_3937.JPG
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Rich WeisslerProfessional Troublemaker^h^h^h^h^hshooterCommented:
The answer is correct, although I don't believe you can assume line AE bisects the angle.  (In this case, it works out that the ratio of the two angles which make up the 48 degree angle are in the same proportion to the interior angle, opposite of x... so your answer for angles ACD and ACB will be wrong, but their sum will be the same.  If you had recognized that this was going to be the same, and used a simplifying assumption -- then good on you.  :-) )
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ExcellearnerAuthor Commented:
Rich, thank you.

I will rework this problem and post my approach. Kindly bear with me.

Thank you
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dhsindyRetired considering supplemental income.Commented:
All you need to know is the sum of the interior angles of a quadrilateral is 360 degrees.

360 - A - D - B = C,  also, it is obvious that C + X = 360.
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