This question nicely illustrates the fact that diagrams on the GRE are not necessarily drawn to scale (see the video below for more on this)

Let's first find the value of ∠G
Since all angles in a triangle add to 180°, we can write: 37° + 53° + ∠G = 180°
Solve to get: ∠G = 90°

Add this to the diagram...

At this point, we can see that the diagram is definitely NOT drawn to scale


In fact, the diagram should look more like this...


Now that we know we have a right triangle, we have two different ways to find the value of x (aka the length of side HI)

1) If we remember our Pythagorean Triplets, we will see that this triangle is a 6-8-10 triangle, which means x = 10

2) Alternatively, we can apply the Pythagorean Theorem to write: 6² + 8² = x²
Simplify: 36 + 64 = x²
Simplify: 100 = x²
Solve: x = √100 = 10

Answer: 10

RELATED VIDEO FROM OUR COURSE

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10. Side HI is not labeled, so inferences will have to be drawn from other
information provided in the figure. Two of the angles of triangle GHI are
labeled, so if the third angle is x°, then 37 + 53 + x = 180. That means x = 90,
and
You should definitely redraw once you discover the
triangle is a right triangle!
Now you can use the Pythagorean theorem to find the length of HI. HI is the
hypotenuse, so (6)2 + (8)2 = c2
, which means 36 + 64 = 100 = c2
, so c = 10.
The length of HI is 10.
Alternatively, recognize the Pythagorean triple: triangle GHI is a 6–8–10 triangle

Angle H + Angle I = 90
So, Angle G = 180 - 90 = 90

Now, by applying the Pythagoras theorem,

HI^2 = HG^2 + GI^2
=> HI^2 = 100
=> HI = 10