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2 years ago

For what values of x and y must the figure have in order to be parallelogram?

Mathematics

1 answer:

Oduvanchick [21]2 years ago

7 0

Answer:

y = 10°

x = 64°

Step-by-step explanation:

Parallelogram is a quadrilateral with the opposite sides parallel to each other. Opposite sides are equal in length. Opposite angles are equal in a parallelogram.

For the figure to be a parallelograms, since opposite angle are equal

12y + 8 = 2x

2x - 12y = 8 ...................(i)

2x + 5y + 2 = 180(supplementary angle)

2x + 5y = 178..............(ii)

combine the equation

2x - 12y = 8 ...................(i)

2x + 5y = 178..............(ii)

make x subject of the formula in equation (i)

2x - 12y = 8 ...................(i)

2x = 8 + 12y

x = 4 + 6y

put the value of x in equation (ii)

2x + 5y = 178..............(ii)

2(4 + 6y) + 5y = 178

8 + 12y + 5y = 178

8 + 17y = 178

17y = 170

divide both sides by 17

y = 170/17

y = 10°

Put the value of y in equation (i)

2x - 12y = 8 ...................(i)

2x - 12(10) = 8

2x - 120 = 8

2x = 128

x = 128/2

x = 64°

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