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To find the value of x, we will use the fact that the sum of the angles in a triangle is 180 degrees.
m∠IHG + m∠IHK + m∠KHG = 180°
Substituting the given values into this equation, we get:
162° + (4x + 4)° + (8x + 2)° = 180°
Combining like terms, we get:
12x + 168 = 180
Solving for x, we get:
12x = 12
x = 1
Therefore, the value of x is 1.