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°
