Answer:
x = 17, see below for angle measures
Step-by-step explanation:
You're on the right track!
The sum of those two angles inside the triangle equal that opposite angle outside of the triangle. Therefore, you can set them equal to each other.
(4x - 8) + (3x - 16) = 95
Because you are adding the expressions, you can take away the parentheses without changing anything.
4x - 8 + 3x - 16 = 95
Now you want to combine like terms on the left side.
4x + 3x - 8 - 16 = 95
7x - 24 = 95
Combine like terms once again.
7x = 119
Divide to isolate x.
x = 119/7
x = 17
Plug this value back into each expression to find the angle measures.
∠HFG = 4x - 8
∠HFG = = 4(17) - 86
∠HFG = 68 - 8
∠HFG = 60º
∠FGH = 3x - 16
∠FGH = 3(17) - 16
∠FGH = 51 - 16
∠FGH = 35º
∠FHI = 95ª
∠FHG = 180 - 95
∠FHG = 85º
