Final answer:
The value of x is 1.
Step-by-step explanation:
To find the value of x in the given question, we need to set up an equation involving the angles.
From the information given, we have:
m∠IHG = 162°
m∠IHK = (4x + 4)°
m∠KHG = (8x + 2)°
We can set up an equation based on the relationship between the angles:
m∠IHG + m∠IHK + m∠KHG = 180°
Substituting the given angle measures, we have:
162° + (4x + 4)° + (8x + 2)° = 180°
Combine like terms:
12x + 168 = 180
Subtract 168 from both sides:
12x = 12
Divide both sides by 12:
x = 1
Therefore, the value of x is 1.