Question

Given: and mEGF∠=60 mAGF∠=°90; Prove: mAGB∠=°30.

Answer 1

Since (unfortunately) I don't recall the specific laws and rules you have to mention in proofs, I can't by any means hand you a copy-and-paste answer; which is a good thing, in the long run. What I can tell you is to group angles and look at the bigger picture, rather than focusing on each angle individually.
When you look at the system of lines and angles as a whole, you can see that the three angles they gave you are significant because they form a straight line, which can give you addition angle measures. You can also see that because the first two givens are next to each other, they can be grouped into a single angle (mEGA<=150) for the purpose of using the pairing rules.
For any problems like these, you want to look for linear pairs, supplementary angles, complementary angles, and adjacent angles that can be grouped to equal another vertical one. Basically, you're looking for enough relational info to set up an equation; in this case: EGF+AGF+AGB=180. Once you can set things equal to each other, all that's left to do is tell what logic you used to get to that point, and then walk through your basic "subtract x from both sides of the equation..." I hope that helps you and others with solving geometry problems! Best of luck & God bless <3