Question

Find the values of x and y that make DEFG a parallelogram

Answer 1

x = 13 (option A), y = 22 (option D)

Step-by-step explanation:

In a parallelogram, the opposite angles are equal

∠G = ∠E

∠D = ∠F

Also any two adjacent angles are supplementary:

∠G + ∠F = 180

∠D + ∠E = 180

∠G = 128, ∠F = 52, ∠D = 4x, ∠E = 6y - 4

∠G = ∠E

128 = 6y - 4

solve for y:

128 + 4 = 6y

132 = 6y

divide both sides by 6:

132/6 = 6y/6

y = 22

∠D = ∠F

4x = 52

divide both sides by 4:

x = 52/4

x = 13

x = 13 (option A), y = 22 (option D)