Given that abcd is an isosceles trapezoid, find x and y.

a. x = 7, y= 10
b. x = 15, y= 10
c. x = 15, y= 40
d. x = 7, y= 40

The answer is C. x=15, y=40
An isosceles trapezoid has equal left and right sides. Thus, to solve for the x:
x-4 = 11
  x = 11+4 (transfer -4 to the right side of the equation)
  x = 15
From the picture, the right side of isosceles trapezoid measures 11. Thus, the left side should also measure 11. Substitute the values to know -
  x-4 = 11
15-4 = 11
   11 = 11

An isosceles trapezoid's any lower base angle is supplementary to any upper base angle or equal to 180 degrees. Thus, to get the value of y -
(4y-20)+ y = 180
             5y = 180 +20 (transfer -20 to the right side of the equation)
             5y = 200
          5y/5 = 200/5 (divide both sides of the equation by 5
               y = 40 degrees
As mentioned, any upper angle plus any lower angle should equal to 180 degrees. Substitute the values to check -
       (4y-20) + y = 180
(4(40)-20) + 40 = 180
          140 + 40 = 180
                  180 = 180