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

Question

Accepted Answer

### 13.
# Explanation:
## Step1: Use angle - addition property
Since $\angle BCD=\angle BCF+\angle FCD$, we have the equation $(x + 78)+(x + 41)=95$.
## Step2: Combine like - terms
$2x+119 = 95$.
## Step3: Isolate the variable term
$2x=95 - 119$, so $2x=-24$.
## Step4: Solve for x
$x=-12$.
# Answer:
$x = - 12$

### 14.
# Explanation:
## Step1: Use the angle - addition property in $	riangle BJK$
In $	riangle BJK$, $\angle BJK=\angle IJB+\angle IJK$. So, $146 + 2x=(2x + 26)+172$.
## Step2: Simplify the right - hand side
$146+2x=2x + 198$.
## Step3: Subtract $2x$ from both sides
$146=198$, which is a contradiction. There is an error in the problem setup. Assuming the correct relationship is based on linear - pair or angle - addition in a different context, if $\angle BJK$ and $\angle IJK$ are related in a non - given correct way, and we consider the exterior - angle property or other geometric relationships. Let's assume the correct equation is $\angle IJK=\angle BJK+\angle IJB$. Then $172=(146 + 2x)+(2x + 26)$.
## Step4: Combine like - terms
$172=172 + 4x$.
## Step5: Solve for x
$4x=0$, so $x = 0$.
# Answer:
$x = 0$

### 15.
# Explanation:
## Step1: Use angle - addition property
Since $\angle GFE=\angle GFZ+\angle ZFE$, we have the equation $x + 163=38+(2x + 125)$.
## Step2: Expand the right - hand side
$x + 163=2x+163$.
## Step3: Subtract $x$ from both sides
$163=x + 163$.
## Step4: Solve for x
$x = 0$.
# Answer:
$x = 0$

### 16.
# Explanation:
## Step1: Use angle - addition property
Since $\angle LMN=\angle LMV+\angle VMN$, we have the equation $135=-1 + 45x+33x$.
## Step2: Combine like - terms
$135=-1 + 78x$.
## Step3: Add 1 to both sides
$136 = 78x$.
## Step4: Solve for x
$x=\frac{68}{39}$.
# Answer:
$x=\frac{68}{39}$

### 17.
# Explanation:
## Step1: Use angle - addition property
Since $\angle HIJ=\angle HIW+\angle WIJ$, we have the equation $145=(2x + 13)+10x$.
## Step2: Combine like - terms
$145=12x + 13$.
## Step3: Subtract 13 from both sides
$132 = 12x$.
## Step4: Solve for x
$x = 11$.
# Answer:
$x = 11$

### 18.
# Explanation:
## Step1: Use angle - addition property
Since $\angle ABC=\angle ABK+\angle KBC$, we have the equation $17x + 8=42+(12x-4)$.
## Step2: Expand the right - hand side
$17x + 8=12x + 38$.
## Step3: Subtract $12x$ from both sides
$5x+8 = 38$.
## Step4: Subtract 8 from both sides
$5x=30$.
## Step5: Solve for x
$x = 6$.
## Step6: Find $\angle ABC$
Substitute $x = 6$ into $\angle ABC=17x + 8$, so $\angle ABC=17	imes6+8=102 + 8=110^{\circ}$.
# Answer:
$\angle ABC = 110^{\circ}$

### 19.
# Explanation:
## Step1: Use angle - addition property
Since $\angle IHG=\angle IHZ+\angle ZHG$, we have the equation $12x + 13=24+(11x-1)$.
## Step2: Expand the right - hand side
$12x + 13=11x + 23$.
## Step3: Subtract $11x$ from both sides
$x+13 = 23$.
## Step4: Subtract 13 from both sides
$x = 10$.
## Step5: Find $\angle IHG$
Substitute $x = 10$ into $\angle IHG=12x + 13$, so $\angle IHG=12	imes10+13=120 + 13=133^{\circ}$.
# Answer:
$\angle IHG = 133^{\circ}$

### 20.
# Explanation:
## Step1: Use angle - addition property
Since $\angle GFE=\angle GFN+\angle NFE$, we have the equation $157=(4x + 10)+(14x+3)$.
## Step2: Combine like - terms
$157=18x + 13$.
## Step3: Subtract 13 from both sides
$144 = 18x$.
## Step4: Solve for x
$x = 8$.
## Step5: Find $\angle NFE$
Substitute $x = 8$ into $\angle NFE=14x + 3$, so $\angle NFE=14	imes8+3=112 + 3=115^{\circ}$.
# Answer:
$\angle NFE = 115^{\circ}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

13.

Step1: Use angle - addition property

Step2: Combine like - terms

Step3: Isolate the variable term

Step4: Solve for x

Step1: Use the angle - addition property in $\triangle BJK$

Step2: Simplify the right - hand side

Step3: Subtract $2x$ from both sides

Step4: Combine like - terms

Step5: Solve for x

Step1: Use angle - addition property

Step2: Expand the right - hand side

Step3: Subtract $x$ from both sides

Step4: Solve for x

Answer:

14.