11) (mangle hgf = 16x + 4), (mangle egf=110^{circ}), and (mangle hge = 3x + 11). find (x). 12) (mangle vut = 175^{circ}), (mangle vuj = 17x - 3), and (mangle jut = 17x + 8). find (x). 13) (mangle fcd=x + 41), (mangle bcf=x + 78), and (mangle bcd = 95^{circ}). find (x). 14) find (x) if (mangle bjk = 146+2x), (mangle ijk = 172^{circ}), and (mangle ijb = 2x + 26). 15) (mangle gfz = 38^{circ}), (mangle zfe = 2x + 125), and (mangle gfe=x + 163). find (x). 16) find (x) if (mangle lmn = 135^{circ}), (mangle lmv=-1 + 45x), and (mangle vmn = 23x). 17) find (mangle hiw) if (mangle wij = 10x), (mangle hij = 145^{circ}), and (mangle hiw = 2x + 13). 18) (mangle abc = 17x + 8), (mangle abk = 42^{circ}), and (mangle kbc = 12x - 4). find (mangle abc). 19) (mangle zhg = 11x - 1), (mangle ihz = 24^{circ}), and (mangle ihg = 12x + 13). find (mangle ihg). 20) (mangle gfn = 4x + 10), (mangle nfe = 14x + 3), and (mangle gfe = 157^{circ}). find (mangle nfe).

Question

Accepted Answer

11)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle HGF=m\angle HGE + m\angle EGF$, we have the equation $16x + 4=(3x + 11)+110$.
## Step2: Simplify the right - hand side
$16x+4 = 3x+121$.
## Step3: Subtract $3x$ from both sides
$16x-3x + 4=3x-3x + 121$, which gives $13x+4 = 121$.
## Step4: Subtract 4 from both sides
$13x+4 - 4=121 - 4$, so $13x=117$.
## Step5: Divide both sides by 13
$x=\frac{117}{13}=9$.
# Answer:
$x = 9$

12)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle VUT=m\angle VUJ+m\angle JUT$, we have the equation $175=(17x - 3)+(17x + 8)$.
## Step2: Simplify the right - hand side
$175=34x + 5$.
## Step3: Subtract 5 from both sides
$175-5=34x+5 - 5$, so $170 = 34x$.
## Step4: Divide both sides by 34
$x=\frac{170}{34}=5$.
# Answer:
$x = 5$

13)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle BCD=m\angle BCF+m\angle FCD$, we have the equation $95=(x + 78)+(x + 41)$.
## Step2: Simplify the right - hand side
$95=2x+119$.
## Step3: Subtract 119 from both sides
$95 - 119=2x+119 - 119$, so $- 24=2x$.
## Step4: Divide both sides by 2
$x=-12$.
# Answer:
$x=-12$

14)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle BJK=m\angle IJB+m\angle IJK$, we have the equation $146 + 2x=(2x + 26)+172$.
## Step2: Simplify the right - hand side
$146 + 2x=2x+198$.
## Step3: Subtract $2x$ from both sides
$146+2x-2x=2x + 198-2x$, $146
eq198$, there is an error. The correct relationship should be $m\angle IJK=m\angle IJB+m\angle BJK$, so $172=(2x + 26)+(146 + 2x)$.
## Step4: Simplify the right - hand side
$172=4x+172$.
## Step5: Subtract 172 from both sides
$172-172=4x+172 - 172$, $0 = 4x$, $x = 0$.
# Answer:
$x = 0$

15)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle GFE=m\angle GFZ+m\angle ZFE$, we have the equation $x + 163=38+(2x + 125)$.
## Step2: Simplify the right - hand side
$x + 163=2x+163$.
## Step3: Subtract $x$ from both sides
$x - x+163=2x - x+163$, $x = 0$.
# Answer:
$x = 0$

16)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle LMN=m\angle LMV+m\angle VMN$, we have the equation $135=(-1 + 45x)+23x$.
## Step2: Simplify the right - hand side
$135=68x-1$.
## Step3: Add 1 to both sides
$135 + 1=68x-1+1$, so $136=68x$.
## Step4: Divide both sides by 68
$x = 2$.
# Answer:
$x = 2$

17)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle HIJ=m\angle HIW+m\angle WIJ$, we have the equation $145=(2x + 13)+10x$.
## Step2: Simplify the right - hand side
$145=12x+13$.
## Step3: Subtract 13 from both sides
$145-13=12x+13 - 13$, so $132=12x$.
## Step4: Divide both sides by 12
$x = 11$.
Then $m\angle HIW=2x + 13=2\times11+13=35^{\circ}$.
# Answer:
$m\angle HIW = 35^{\circ}$

18)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle ABC=m\angle ABK+m\angle KBC$, we have the equation $17x + 8=42+(12x - 4)$.
## Step2: Simplify the right - hand side
$17x + 8=12x+38$.
## Step3: Subtract $12x$ from both sides
$17x-12x + 8=12x-12x+38$, $5x+8 = 38$.
## Step4: Subtract 8 from both sides
$5x+8 - 8=38 - 8$, so $5x=30$.
## Step5: Divide both sides by 5
$x = 6$.
Then $m\angle ABC=17x + 8=17\times6+8=110^{\circ}$.
# Answer:
$m\angle ABC = 110^{\circ}$

19)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle IHG=m\angle IHZ+m\angle ZHG$, we have the equation $12x + 13=24+(11x - 1)$.
## Step2: Simplify the right - hand side
$12x + 13=11x+23$.
## Step3: Subtract $11x$ from both sides
$12x-11x + 13=11x-11x+23$, $x+13 = 23$.
## Step4: Subtract 13 from both sides
$x=10$.
Then $m\angle IHG=12x + 13=12\times10+13=133^{\circ}$.
# Answer:
$m\angle IHG = 133^{\circ}$

20)
# Explanation:
## Step1: Use angle - addition property
Since $m\angle GFE=m\angle GFN+m\angle NFE$, we have the equation $157=(4x + 10)+(14x + 3)$.
## Step2: Simplify the right - hand side
$157=18x+13$.
## Step3: Subtract 13 from both sides
$157-13=18x+13 - 13$, so $144=18x$.
## Step4: Divide both sides by 18
$x = 8$.
Then $m\angle NFE=14x + 3=14\times8+3=115^{\circ}$.
# Answer:
$m\angle NFE = 115^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use angle - addition property

Step2: Simplify the right - hand side

Step3: Subtract \(3x\) from both sides

Step4: Subtract 4 from both sides

Step5: Divide both sides by 13

Step1: Use angle - addition property

Step2: Simplify the right - hand side

Step3: Subtract 5 from both sides

Step4: Divide both sides by 34

Step1: Use angle - addition property

Step2: Simplify the right - hand side

Step3: Subtract 119 from both sides

Step4: Divide both sides by 2

Answer: