Answer
X = 10
Y = 20
Step by step
Angle EJF is 90 degrees because EJF is a right angle as indicated by the right angle square. We have numbers for all three angles in the supplementary angle made by line FH.
We know the supplementary angle will equal 180 degrees.
So we can use the equation
3y + 8 + 22 + 90 = 180
Combine like terms
3y + 120 = 180
Subtract 120 from both sides to isolate the variable
3y + 120 - 120 = 180 - 120
Combine
3y = 60
Divide both sides by 3 to solve for y
3/3 y = 60/3
y = 20
Now we can solve for angle DJH by substituting 20 for y
3y + 8
3(20) + 8
60 + 8 = 68
Angle DJH = 68
We see angle FJG is a vertical angle to DJH, so they are congruent or the same.
So FJG = DJH (measures 68)
Knowing this we can solve for x with the equation
8x - 12 = 68
Add 12 to both sides to isolate the variable
8x - 12 + 12 = 68 + 12
Combine
8x = 80
Divide both sides by 8 to solve for x
8/8 x = 80/8
x = 10