Find the value of each variable so that the quadrilateral is a parallelogram.
1 answer:
Answer:
<em>x = -2</em>
<em>y = -5</em>
Step-by-step explanation:
<u>Properties of a Parallelogram</u>
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
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