Studying Mathematics Thread

[GrandizerII]

The first stage of the solution should be something like this:

https://pasteboard.co/HKpm2E7.png

Basic stuff really, so anyone with just a basic familiarity with solving angles should get this part right.

Now, for the next stage, it should be like this:

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https://image.ibb.co/fxjVv0/Stage-2.png

Note line DF parallel to AB was drawn. With parallel lines, corresponding angles are equal. Hence, we can know the measures of the angles CDF and CFD. Consequently, we can also know the measures of their respective supplementary angles ADF and BFD. Colors help indicate the exact spaces for some of the depicted angles. Also, some of the measures noted in the earlier image were removed in this one to make sure things are kept relatively neat.

Next stage should be like this:
https://image.ibb.co/dDOO50/Stage-3.png

Note image clearly not drawn to scale. In this stage, another line was drawn from A to F.

Since triangle CAB is isosceles, and CDF is similar to CAB (therefore, CDF is also isosceles), then the length of DA is equal to the length of FB. You will have to do some algebra to confirm this for yourself. But once you figure that out, you can then deduce that triangle FDA is congruent to triangle DFB (SAS congruency). We then can determine that the measure of angle AFD (being the same as that of BDF) is equal to 60. Therefore, triangle DFG is equilateral, and the measure of angle DGF is 60.

Angle AGB is opposite to angle DGF, therefore its measure is 60. Hence, we can also deduce triangle ABG is also equilateral.

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Solution not fully done yet, but I'll get to posting the continuation later.