Question

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

Answer 1

solutions are

`x=(173)/(7)`

`y=(166)/(7)`

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=(166)/(7)`

now, we can find x

`x=(166)/(7)+1`

`x=(173)/(7)`

So, solutions are

`x=(173)/(7)`

`y=(166)/(7)`

Answer 2

x=11,y=10.

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.