you know that if one line is perpendicular to another line, and another line is perpendicular to that line, they are all perpendicular (90). so, all corners are right angles. that means that angle AGD is 90. so, if you know 30, then subtract 30 from 90 and you get that angle AGF is 60. then, because angle AGF and angle EGB are vertical angles, they are congruent, so x is 60.
