Question

Find the value of each variable in the parallelogram

Answer 1

7.) y=8, x=7

8.) y=3, x=11

9.) h=65, k=10

Explanation:

First, let's start with #7. By definition of a parallelogram, we can say that opposite sides are congruent, meaning 2y-7=9 and 3x+2=23.

So, solving these problems-

2y-7=9

2y=16

y=8

3x+2=23

3x=21

x=7

Now, let's move on to #8. For this, a defining property of a parallelogram is that the diagonals bisect each other. So, 3y+5=14 and 2x-5=17.

Let's solve these equations-

3y+5=14

3y=9

y=3

2x-5=17

2x=22

x=11

Now, finally #9. Another defining property of a parallelogram is that opposite angles are congruent. So, 2h=130 and 5k=50.

So, h= 65 and k= 10.

Answer 2

Alright.

For 7, you'll want to put congruent sides equal to each other, assuming they are parallelograms. So, you'll get the two equations:

3x+2=23

2y-7=9

Solve using GEMDAS/PEMDAS, and you'll get these answers.

3x+2=23

3x=21

x=7

2y-7=9

2y=2

y=1

For 8, you'll want to do the exact same thing, formatting the numbers to equal each other. You'll get these two equations:

3y+5=14

2x-5=17

Solving them would make:

3y+5=14

3y=9

y=3

2x-5=17

2x=22

x=11

For 9, you have to remember that the angle opposite of one angle in a defined parallelogram are congruent. Thus:

130=2h

5k=50

solve them and you get

h=65

k=10

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Hope that helped. Good luck.