Answer:
y = 52
x = 30
Step-by-step explanation:
Hi!
Y is a vertical angle. See <DOB? That's it's vertical pair. So, y = 2x - 8 [vertical angles are congruent].
Now, to find y, we need x. We can find x by using the fact that AB is a straight line. The angles on a straight line add up to 90.
Given the fact that <AOB is 90 degrees, <EOB also has to be 90 degrees.
So, EOB = 90 degrees. Remember that an angle is equal to the sum of the measures of the angles that it is made of.
EOB is therefore equal to <EOD + <DOB.
90 = <EOD + DOB
90 = (x +8) + (2x-8)
90 = 3x
x = 30
Check:
38 + 52 = 90.
So, x = 30
Now, we go back to find y.
y = 2x-8
y = 52
