Question

Find the value of each variable so that the quadrilateral is a parallelogram.

-2x + 6
X+ 12
y + 23
X =
y =

Answer 1

x = -2

y = -5

Explanation:

Properties of a Parallelogram

• Two pairs of opposite sides are parallel.
• Two pairs of opposite sides are equal in length.
• Two pairs of opposite angles are equal in measure
• The diagonals bisect each other.
• Adjacent angles are supplementary.
• Each diagonal divides the quadrilateral into two congruent triangles.

Each diagonal is divided into two measures expressed with variables. Since diagonals bisect each other:

y + 23 = -4y - 2. And

-2x + 6 = x + 12

Solve the first equation. Adding 4y:

5y + 23 = - 2

Subtracting 23:

5y = -25

Dividing by 5:

y = -5

Solve the second equation. Subtracting x and 6:

-3x = 6

Dividing by -3:

x = -2

Solution:

x = -2

y = -5