Finding angle measures between intersecting lines

Answer:
x = 13⁰
Step-by-step explanation:
Since AGC is a right angle, AGD is also a right angle
(Sum of angles of straight line is 180, 180 - 90 =90)
Now, DGF + 77 = 90
or, DGF = 90 - 77
DGF = 13
Now we can say that DGF = x because opposite angles formed by intersecting lines are always equal.
So, x = 13⁰
Answer:
Step-by-step explanation:
∠EGB = 77 {Vertically opposite angles}
∠CGB = 90°
∠CGE + ∠EGB = ∠CGB
x + 77 = 90
x = 90 - 77
x = 13