Answer:
x = 8
Step-by-step explanation:
This question tests on the concept of angle properties and possibly solving equations.
Lets first find Angle FHG in terms of x.
FHG + 80 + (x + 12) = 180 (Sum of Angles in a triangle)
FHG = 180 - 80 - 12 - x = 88 - x
Now we also know another property:
Angle AHG + FHG = 180 (Sum of Angles on a straight line)
Now we can substitute both angles to find x.
11x + 12 + (88 - x) = 180
11x + 12 + 88 - x = 180
10x + 100 = 180
10x = 180 - 100
10x = 80
x = 80 ÷ 10 = 8
