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Use the picture below of parallelogram MNPR to answer the question below.What is the sum of x and y?

Use the picture below of parallelogram MNPR to answer the question below.What is the-example-1

1 Answer

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The parallelogram is a 4 sided figure whose opposite angles and sides are equal. As such, from the given image we may deduct that

4y - 9 = 2x + 19

and

5x = 2y + 1

from

4y - 9 = 2x + 19

4y = 2x + 19 + 9

4y = 2x + 28

Divide both sides by 2

2y = x + 14

From 5x = 2y + 1

2y = 5x - 1

equating the 2 derived equations

x + 14 = 5x - 1

collect like terms

5x - x = 14 + 1

4x = 15

Divide both sides by 4

x = 15/4

= 3.75

2y = 5 (15/4) - 1

2y = 75/4 - 1

2y = 71/4

divide both sides by 2

y = 71/8

Hence x + y

= 15/4 + 71/8

= 30/8 + 71/8

= 101/8

= 12.625

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