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Find the value of the variables in the given parallelogram.

Find the value of the variables in the given parallelogram.-example-1

1 Answer

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Answer:

x = 58, y = 61

Explanation:

We can use two properties of a parallelogram to solve this

1. The opposite angles of a parallelogram are equal

2. The sum of the 4 interior angles of a parallelogram equal 360

Using property 1,

  • the angle opposite angle y is also y(bottom left)
  • 2x + 3 = y + x
    Therefore 2x -x - y = -3 or x - y = -3 [1]

Using property 2
(2x - 3) + y + (y + x) + y = 360

3x + 3y + 3 = 360

3x + 3y = 360 - 3 = 357

Divide both sides by 3 to get
x + y = 357/3
x + y = 119 [2]

Add [1] and [2] together to eliminate y and get

x - y + x + y = -3 + 119

2x = 116

x = 116/2 = 58

Use equation [2]

x + y = 119
58 + y = 119

y = 119 - 58

y = 61

User Stefan Arn
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