Question

Find the measurement indicated in each parallelogram.

Answer 1

Answer:

9. m∠v = 50°

10. m∠EFG = 60°

11. SU = 32

12. m∠G = 70°

13. m∠KMN = 37°

14. m∠CDE = 40°

Step-by-step explanation:

9.

36x - 1 + 29x + 1 + 50 = 180

36x + 29x = 65x

-1 + 1 = 0

65x + 50 = 180

65x + 50 - 50 = 180 - 50

65x = 130

65x/65 = 130/65

x = 2

m∠v = m∠x

m∠v = 50°

10.

x + 120 + 26 + 2x + 34 = 180

Step 1: Simplify both sides of the equation.

x+120+26+2x+34=180

(x+2x)+(120+26+34)=180(Combine Like Terms)

3x+180=180

3x+180=180

Step 2: Subtract 180 from both sides.

3x+180−180=180−180

3x=0

Step 3: Divide both sides by 3.

3x/3 = 0/3

x = 0

m∠EFG = 180 - m∠E

= 180 - (x + 120)

= 180 - (0 + 120)

= 180 - 120

= 60

m∠EFG = 60°

11.

2x − 2 = x + 7

Step 1: Subtract x from both sides.

2x−2−x=x+7−x

x−2=7

Step 2: Add 2 to both sides.

x−2+2=7+2

x=9

SU = 2(QU)

= 2(x + 7)

= 2(9 + 7)

= (2)(16)

= 32

SU = 32

12.

5x+10+44+4x+18=180

Step 1: Simplify both sides of the equation.

5x+10+44+4x+18=180

(5x+4x)+(10+44+18)=180(Combine Like Terms)

9x+72=180

9x+72=180

Step 2: Subtract 72 from both sides.

9x+72−72=180−72

9x=108

Step 3: Divide both sides by 9.

9x/9 = 108/9

x = 12

m∠G = m∠E

m∠G = 5x + 10

m∠G = 5(12) + 10

m∠G = 70°

13. 10x + 5 + 38 + 4x - 3 = 180

10x+5+38+4x−3=180

Step 1: Simplify both sides of the equation.

10x+5+38+4x−3=180

10x+5+38+4x+−3=180

(10x+4x)+(5+38+−3)=180(Combine Like Terms)

14x+40=180

14x+40=180

Step 2: Subtract 40 from both sides.

14x+40−40=180−40

14x=140

Step 3: Divide both sides by 14.

14x/14 = 140/14

x = 10

m∠KMN = 4x - 3

= 4(10) - 3

= 40 - 3

= 37

m∠KMN = 37°

14. 29x - 5 + 5x + 15 = 180

Step 1: Simplify both sides of the equation.

29x−5+5x+15=180

29x+−5+5x+15=180

(29x+5x)+(−5+15)=180(Combine Like Terms)

34x+10=180

34x+10=180

Step 2: Subtract 10 from both sides.

34x+10−10=180−10

34x=170

Step 3: Divide both sides by 34.

34x/34 = 170/34

x = 5

m∠CDE = 5x + 15

= 5(5) + 15

= 25 + 15

= 40

m∠CDE = 40°