Question

For what values of x and y must each figure be a parallelogram?

Answer 1

Answer:

solutions are

$x=\frac{173}{7}$

$y=\frac{166}{7}$

Step-by-step explanation:

We are given that

it is parallelogram

so, alternate angles must be equal

Since, it is parallelogram

so, sum of alternate  angles must be 180

we get

$x+9+2y+2x+2y+2=180$

we will get equation as

$x+2y+2x+2y+11=180$

$3x+4y+11=180$

$3x+4y=169$

we know that diagonal bisect angles

so, we get

$2x=2y+2$

now, we can solve for x

$x=y+1$

now, we can plug this into first equation

$3(y+1)+4y=169$

now, we can solve for y

$7y+3=169$

$y=\frac{166}{7}$

now, we can find x

$x=\frac{166}{7}+1$

$x=\frac{173}{7}$

So, solutions are

$x=\frac{173}{7}$

$y=\frac{166}{7}$

Answer 2

Answer:

x=11,y=10.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.

We can form an equation in x and y using this property.

2y+2=2x

and x+9=2y.

Solving the second  equation for x ,

x=2y-9.

Substituting x value in 2y+2=2x

2y+2=2(2y-9)

Or ,2y+2=4y-18.

Adding 18 both sides:

2y+20=4y.

Subtracting 2y both sides

20=2y.

Dividing both sides by 2:

y=10.

x=2y-9

x=2(10)-9 ( substituting y value)

x=20-9=11

x=11 and y=10 will make the figure a parallelogram.