find the indicated angle measure.
1. find m∠lmn
2. ∠ghk is a straight angle. find m∠lhk
3. m∠abc = 95°. find m∠abd and m∠dbc
4. m∠xyz = 117°. find m∠xyw and m∠wyz
5. ∠lmn is a straight angle. find m∠lmp and m∠nmp
6. ∠abc is a straight angle. find m∠abx and m∠cbx
7. find m∠rsq and m∠tsq
8. find m∠deh and m∠feh

Question

Accepted Answer

1.
# Explanation:
## Step1: Combine angle measures
Since $\angle LMN=\angle LMP+\angle PMN$, and $\angle LMP = 85^{\circ}$, $\angle PMN=23^{\circ}$, then $m\angle LMN=85^{\circ}+ 23^{\circ}$.
$m\angle LMN=108^{\circ}$
# Answer:
$m\angle LMN = 108^{\circ}$

2.
# Explanation:
## Step1: Use straight - angle property
A straight angle $\angle GHK = 180^{\circ}$. Given $\angle GHL=79^{\circ}$, and $\angle GHK=\angle GHL+\angle LHK$. So $m\angle LHK=180^{\circ}-\angle GHL$.
$m\angle LHK = 180 - 79=101^{\circ}$
# Answer:
$m\angle LHK = 101^{\circ}$

3.
# Explanation:
## Step1: Set up an equation
Since $\angle ABC=\angle ABD+\angle DBC$, and $\angle ABC = 95^{\circ}$, $\angle ABD=(2x + 23)^{\circ}$, $\angle DBC=(9x-5)^{\circ}$. Then $(2x + 23)+(9x - 5)=95$.
## Step2: Simplify the equation
Combine like - terms: $2x+9x+23 - 5=95$, which gives $11x+18 = 95$.
## Step3: Solve for x
Subtract 18 from both sides: $11x=95 - 18=77$. Then $x = 7$.
## Step4: Find angle measures
$m\angle ABD=2x+23=2	imes7 + 23=14 + 23=37^{\circ}$
$m\angle DBC=9x-5=9	imes7-5=63 - 5=58^{\circ}$
# Answer:
$m\angle ABD = 37^{\circ}$, $m\angle DBC = 58^{\circ}$

4.
# Explanation:
## Step1: Set up an equation
Since $\angle XYZ=\angle XYW+\angle WYZ$, and $\angle XYZ = 117^{\circ}$, $\angle XYW=(6x + 44)^{\circ}$, $\angle WYZ=(-10x + 65)^{\circ}$. Then $(6x + 44)+(-10x + 65)=117$.
## Step2: Simplify the equation
Combine like - terms: $6x-10x+44 + 65=117$, which gives $-4x+109 = 117$.
## Step3: Solve for x
Subtract 109 from both sides: $-4x=117 - 109 = 8$. Then $x=-2$.
## Step4: Find angle measures
$m\angle XYW=6x + 44=6	imes(-2)+44=-12 + 44=32^{\circ}$
$m\angle WYZ=-10x + 65=-10	imes(-2)+65=20 + 65=85^{\circ}$
# Answer:
$m\angle XYW = 32^{\circ}$, $m\angle WYZ = 85^{\circ}$

5.
# Explanation:
## Step1: Set up an equation
Since $\angle LMN$ is a straight angle ($180^{\circ}$) and $\angle LMN=\angle LMP+\angle NMP$, with $\angle LMP=(-16x + 13)^{\circ}$ and $\angle NMP=(-20x + 23)^{\circ}$. Then $(-16x + 13)+(-20x + 23)=180$.
## Step2: Simplify the equation
Combine like - terms: $-16x-20x+13 + 23=180$, which gives $-36x+36 = 180$.
## Step3: Solve for x
Subtract 36 from both sides: $-36x=180 - 36 = 144$. Then $x=-4$.
## Step4: Find angle measures
$m\angle LMP=-16x + 13=-16	imes(-4)+13=64 + 13=77^{\circ}$
$m\angle NMP=-20x + 23=-20	imes(-4)+23=80 + 23=103^{\circ}$
# Answer:
$m\angle LMP = 77^{\circ}$, $m\angle NMP = 103^{\circ}$

6.
# Explanation:
## Step1: Set up an equation
Since $\angle ABC$ is a straight angle ($180^{\circ}$) and $\angle ABC=\angle ABX+\angle CBX$, with $\angle ABX=(14x + 70)^{\circ}$ and $\angle CBX=(20x + 8)^{\circ}$. Then $(14x + 70)+(20x + 8)=180$.
## Step2: Simplify the equation
Combine like - terms: $14x+20x+70 + 8=180$, which gives $34x+78 = 180$.
## Step3: Solve for x
Subtract 78 from both sides: $34x=180 - 78 = 102$. Then $x = 3$.
## Step4: Find angle measures
$m\angle ABX=14x + 70=14	imes3+70=42 + 70=112^{\circ}$
$m\angle CBX=20x + 8=20	imes3+8=60 + 8=68^{\circ}$
# Answer:
$m\angle ABX = 112^{\circ}$, $m\angle CBX = 68^{\circ}$

7.
# Explanation:
## Step1: Set up an equation
Let $\angle RSQ=(15x - 43)^{\circ}$ and $\angle TSQ=(8x + 18)^{\circ}$. Since $\angle RST=\angle RSQ+\angle TSQ$, assume $\angle RST$ is a right - angle ($90^{\circ}$) (not given explicitly in the problem statement, but a common case for such angle - splitting problems). Then $(15x - 43)+(8x + 18)=90$.
## Step2: Simplify the equation
Combine like - terms: $15x+8x-43 + 18=90$, which gives $23x-25 = 90$.
## Step3: Solve for x
Add 25 to both sides: $23x=90 + 25=115$. Then $x = 5$.
## Step4: Find angle measures
$m\angle RSQ=15x - 43=15	imes5-43=75 - 43=32^{\circ}$
$m\angle TSQ=8x + 18=8	imes5+18=40 + 18=58^{\circ}$
# Answer:
$m\angle RSQ = 32^{\circ}$, $m\angle TSQ = 58^{\circ}$

8.
# Explanation:
## Step1: Set up an equation
Let $\angle DEH = 13x^{\circ}$ and $\angle FEH=(10x + 21)^{\circ}$. Assume $\angle DEF$ is a right - angle ($90^{\circ}$) (not given explicitly, but a common case). Then $13x+(10x + 21)=90$.
## Step2: Simplify the equation
Combine like - terms: $13x+10x+21=90$, which gives $23x+21 = 90$.
## Step3: Solve for x
Subtract 21 from both sides: $23x=90 - 21=69$. Then $x = 3$.
## Step4: Find angle measures
$m\angle DEH=13x=13	imes3=39^{\circ}$
$m\angle FEH=10x + 21=10	imes3+21=30 + 21=51^{\circ}$
# Answer:
$m\angle DEH = 39^{\circ}$, $m\angle FEH = 51^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Combine angle measures

Step1: Use straight - angle property

Step1: Set up an equation

Step2: Simplify the equation

Step3: Solve for x

Step4: Find angle measures

Answer: