Question

Quadrilateral ABCD has these angle measures:

mzA= 124°
mzB = (8x - 2y)
mzC=(16x-7y)°
m2D = 56°
What values of x and y make ABCD a parallelogram?
x=6 and y=-4
x = -6 and y=-4
x = 6 and y = 4
x = -6 and y = 4

Answer 1

x=6 and y = -4

Explanation:

Opposite angles of a parallelogram are congruent so:

• Angle A is congruent to Angle C
• 124 = 16x - 7y
• 16x = 124 + 7y

• Angle B is congruent to angle D
• 8x - 2y = 56
• 8x = 56 + 2y
• 16x = 112 + 4y

This means that:

• 112 + 4y = 124 + 7y
• 4y = 12 + 3y
• -3y = 12
• y = -4

So, 16x = 124+7(-4) = 96, meaning x=6