9) solve for x. 10) 11) 12) find the measure of the angle indicated in bold. 13) 14) 15)

Question

Accepted Answer

### 9)
# Explanation:
## Step1: Identify angle - relationship
The two angles are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So the unknown angle is also 127°.
# Answer:
127°

### 10)
# Explanation:
## Step1: Set up the equation
Since the two angles are corresponding angles (formed by parallel lines and a transversal), they are equal. So we set up the equation $10x + 15=115$.
## Step2: Solve for $x$
Subtract 15 from both sides: $10x=115 - 15=100$. Then divide both sides by 10: $x = \frac{100}{10}=10$.
# Answer:
$x = 10$

### 11)
# Explanation:
## Step1: Set up the equation
The two angles are corresponding angles (formed by parallel lines and a transversal), so $8x + 12=- 10+10x$.
## Step2: Solve for $x$
Subtract $8x$ from both sides: $12=-10 + 10x-8x$, which simplifies to $12=-10 + 2x$. Then add 10 to both sides: $2x=12 + 10=22$. Divide both sides by 2: $x = 11$.
# Answer:
$x = 11$

### 12)
# Explanation:
## Step1: Set up the equation
The two angles are corresponding angles (formed by parallel lines and a transversal), so $x + 68=60$.
## Step2: Solve for $x$
Subtract 68 from both sides: $x=60 - 68=-8$.
# Answer:
$x=-8$

### 13)
# Explanation:
## Step1: Set up the equation
The two angles are corresponding angles (formed by parallel lines and a transversal), so $10x + 10=17x+8$.
## Step2: Solve for $x$
Subtract $10x$ from both sides: $10=17x + 8-10x$, which simplifies to $10 = 7x+8$. Then subtract 8 from both sides: $7x=10 - 8 = 2$. Divide both sides by 7: $x=\frac{2}{7}$.
## Step3: Find the measure of the bold - indicated angle
Substitute $x = \frac{2}{7}$ into $10x + 10$: $10\times\frac{2}{7}+10=\frac{20}{7}+10=\frac{20 + 70}{7}=\frac{90}{7}\approx12.86^{\circ}$
# Answer:
$\frac{90}{7}^{\circ}$

### 14)
# Explanation:
## Step1: Set up the equation
The two angles are corresponding angles (formed by parallel lines and a transversal), so $15x-6=13x + 10$.
## Step2: Solve for $x$
Subtract $13x$ from both sides: $15x-13x-6=10$, which simplifies to $2x-6 = 10$. Then add 6 to both sides: $2x=10 + 6=16$. Divide both sides by 2: $x = 8$.
## Step3: Find the measure of the bold - indicated angle
Substitute $x = 8$ into $15x-6$: $15\times8-6=120 - 6=114^{\circ}$
# Answer:
$114^{\circ}$

### 15)
# Explanation:
## Step1: Set up the equation
The two angles are corresponding angles (formed by parallel lines and a transversal), so $x + 67=x + 127$. This is a contradiction. There is likely an error in the problem - setup as these two expressions for angles cannot be equal for real - valued $x$. If we assume they are same - side interior angles (supplementary), then $(x + 67)+(x + 127)=180$.
## Step2: Solve for $x$
Combine like terms: $2x+194 = 180$. Subtract 194 from both sides: $2x=180 - 194=-14$. Divide both sides by 2: $x=-7$.
# Answer:
$x=-7$

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QUESTION IMAGE

Question

Explanation:

9)

Step1: Identify angle - relationship

Step1: Set up the equation

Step2: Solve for \(x\)

Step1: Set up the equation

Step2: Solve for \(x\)

Answer:

10)