In a parallelogram, the opposite angles will be congruent to each other.
In this parallelogram, angles B and C are congruent, and angles A and D are congruent.
We will work on angles B and C first. Set the two angles to equal each other:
[tex] 12x + 6 = 6x + 66 [/tex]
Subtract 6 from both sides:
[tex] 12x = 6x + 60 [/tex]
Subtract 6x from both sides:
[tex] 6x = 60 [/tex]
Divide both sides by 6 to get x by itself:
[tex] \boxed{x = 10} [/tex]
x will equal 10.
Set angles A and D to equal each other:
[tex] 54 = 3y [/tex]
Divide both sides by 3 to get y by itself:
[tex] \boxed{y = 18} [/tex]
y will equal 18.
The x and y values that make this quadrilateral a parallelogram will be x = 10, and y = 18.
