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Korolek [52]
2 years ago
13

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

Mathematics
1 answer:
Dmitry [639]2 years ago
4 0

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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