Let's start with x... Since angle AOE is a 90 degree angle, then we know the supplementary angle EOB is also 90 degrees. The 2 angles that make up angle EOB are given to us as expressions. Added together the must equal 90 degrees...
(x+8) + (2x-8) = 90 3x = 90 x = 30
Now if we look at y, we see it is an opposite angle from angle DOB. Because it is opposite, it is also congruent... so it has to be equal to angle DOB... and since angle DOB is 2x - 8, we can substitute x with the answer we found in the last step, 30, to find the angle.
2x - 8= y 2(30) - 8 = y 60 - 8 = y y = 52 degrees
Since angle DOB equals 52 degrees, then y = 52 degrees
x = 30 degrees y = 52 degrees
*Note, you can also find the value of angles GOF and EOD by plugging x (30) into the expressions.
