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Triangle - computing angles

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

The figure, given alongside, shows a triangle ABC whose sides AB and AC are produced upto D a nd E respectively. The bisectors of exterior angles so formed intersect each other at point I. If Ang BAC = 80d and Ang ACB = 50d, find:
1.      Ang ECB
2.      Ang DBC
3.      Ang ICB
4.      Ang IBC
5.      Ang BIC

Kindly let me know if any theorem is available which explains the geometric properties of this triangle.
Ang  =Angle
1 Solution
Paul SauvéCommented:
1-sum of the angles of a triangle = 180° = ACB+CAB+ABC
2-two angles are supplementary if the sum of their angles equals 180° = ACB + ECB = ABC+DBC
3-the bisectors of an angle divides the angle int 2 equal parts

this is sufficient information to solve for angles ECB, DBC, ICB, IBC and BIC
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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