use the diagram below to complete 10-12. (diagram not drawn to scale).
10.) identify the relationship of the two angles written in terms of x.
(5x+40)°
(7x)°
11.) write an equation using the two angles written in terms of x, and then solve for x. (show your work!)
12.) what is the measure of each angle written in terms of x? (show your work!)
use the diagram below to complete 13-15. (diagram not drawn to scale).
13.) identify the relationship of the two angles written in terms of y.
(7y)°
(5y)°
14.) write an equation using the two angles written in terms y, and then solve for y. (show your work!)
15.) what is the measure of the two angles that are written in terms of y? (show your work!)

Question

Accepted Answer

### Question 10:
# Explanation:
## Step1: Analyze the diagram
The two angles $(5x + 40)^{\circ}$ and $(7x)^{\circ}$ are formed by a transversal intersecting two parallel lines. From the diagram, we can see that these two angles are alternate exterior angles (or we can also observe that they are equal because of the parallel lines and transversal, so they are congruent).
## Step2: Identify the relationship
Since the lines are parallel, the two angles are equal (congruent) as they are alternate exterior angles (or corresponding angles in some cases, but from the position, alternate exterior angles which are equal when lines are parallel). So the relationship is that they are equal (congruent) angles.
# Answer:
The two angles $(5x + 40)^{\circ}$ and $(7x)^{\circ}$ are equal (congruent) angles (alternate exterior angles formed by a transversal intersecting two parallel lines).

### Question 11:
# Explanation:
## Step1: Set up the equation
Since the two angles are equal (from question 10), we can set up the equation $5x + 40=7x$.
## Step2: Solve for $x$
Subtract $5x$ from both sides of the equation:
$5x + 40-5x=7x - 5x$
$40 = 2x$
Divide both sides by 2:
$x=\frac{40}{2}=20$
# Answer:
The equation is $5x + 40 = 7x$, and $x = 20$.

### Question 12:
# Explanation:
## Step1: Find the measure of $(5x + 40)^{\circ}$
Substitute $x = 20$ into $5x+40$:
$5\times20 + 40=100 + 40 = 140^{\circ}$
## Step2: Find the measure of $(7x)^{\circ}$
Substitute $x = 20$ into $7x$:
$7\times20=140^{\circ}$
# Answer:
The measure of $(5x + 40)^{\circ}$ is $140^{\circ}$ and the measure of $(7x)^{\circ}$ is $140^{\circ}$.

### Question 13:
# Explanation:
## Step1: Analyze the diagram
The two angles $(7y)^{\circ}$ and $(5y)^{\circ}$ are formed by a transversal intersecting two parallel lines. From the diagram, we can see that these two angles are same - side interior angles (or we can observe that they are supplementary because of the parallel lines and transversal, so their sum is $180^{\circ}$).
## Step2: Identify the relationship
Since the lines are parallel, the two angles are supplementary (their sum is $180^{\circ}$) as they are same - side interior angles.
# Answer:
The two angles $(7y)^{\circ}$ and $(5y)^{\circ}$ are supplementary angles (their sum is $180^{\circ}$) as they are same - side interior angles formed by a transversal intersecting two parallel lines.

### Question 14:
# Explanation:
## Step1: Set up the equation
Since the two angles are supplementary (from question 13), we can set up the equation $7y+5y = 180$.
## Step2: Solve for $y$
Combine like terms: $12y=180$
Divide both sides by 12: $y=\frac{180}{12} = 15$
# Answer:
The equation is $7y + 5y=180$, and $y = 15$.

### Question 15:
# Explanation:
## Step1: Find the measure of $(7y)^{\circ}$
Substitute $y = 15$ into $7y$:
$7\times15 = 105^{\circ}$
## Step2: Find the measure of $(5y)^{\circ}$
Substitute $y = 15$ into $5y$:
$5\times15=75^{\circ}$
# Answer:
The measure of $(7y)^{\circ}$ is $105^{\circ}$ and the measure of $(5y)^{\circ}$ is $75^{\circ}$.

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QUESTION IMAGE

Question

Explanation:

Question 10:

Step1: Analyze the diagram

Step2: Identify the relationship

Step1: Set up the equation

Step2: Solve for \(x\)

Step1: Find the measure of \((5x + 40)^{\circ}\)

Step2: Find the measure of \((7x)^{\circ}\)

Answer:

Question 11: