Answer: 60
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Step-by-step explanation:
Angles EGD and BGF are vertical angles. Both are unknown and equal to x.
Notice how angle AGD is adjacent to angle CGD. These two angles form a straight angle (180 degrees) and angle CGD is a right angle. That must mean AGD is also a right angle.
Angles AGE and EGD must add to 90 degrees since AGD is 90
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(angleAGE)+(angleEGD) = (angle AGD)
(30) + (x) = 90
x = 90-30
x = 60