Answer:
60.4°
Step-by-step explanation:
DF is a line, which means ∠DEF = 180°. We also know that ∠DEF = ∠DEB + ∠BEG + ∠GEF. We already know three of these measures, so we can solve for the other:
∠DEF = ∠DEB + ∠BEG + ∠GEF
180 = 110.2 + ∠BEG + 25.6
∠BEG = 44.2°
We know that lines AC and DF are parallel, and since ∠ABE and ∠BEF are alternate interior angles, by definition, ∠ABE = ∠BEF.
∠BEF = ∠BEG + ∠GEF = 44.2 + 25.6 = 69.8°
Then, ∠ABE = ∠BEF = 69.8°.
Again, since AC is a line, ∠ABC = 180°. We also know that ∠ABC = ∠ABE + ∠EBG + ∠GBC. Just like before, we already know three of these angles, so we can solve for the other:
∠ABC = ∠ABE + ∠EBG + ∠GBC
180 = 69.8 + ∠EBG + 34.8
∠EBG = 75.4°
Finally, since EBG is a triangle, we know that its interior angles add up to 180:
∠BEG + ∠EBG + ∠BGE = 180
Plug in the values we know:
44.2 + 75.4 + x = 180
x = 60.4°
