items 11 - 15. lines a, b, c and d intersect as shown.
11. which pair of lines are parallel?
a a and b
b a and c
c c and d
d b and d
12. what is x?
13. what is y?
a 42
b 85
c 88
d 95
14. what is z?
a 88
b 92
c 95
d 124
15. if the slope of line c is given, the slope of which other line is known?
16. what is the equation of a line that is parallel to the line y = 2x+7 and passes through the point (-2, 4)?
a y=-\frac{1}{2}x + 3
b y = 2x+4
c y=-\frac{1}{2}x - 2
d y = 2x+8
17. what is the slope of a line perpendicular to the line y=-\frac{3}{4}x - 1?
items 18 - 20. part of a city map is shown.
18. which street is parallel to 1st ave?
a 2nd ave
b main road
c central ave
d d street
19. a city road planner wants to build a road perpendicular to d street. what is the slope of the new road?
20. if m\angle5=x, which angles also have a measure of x? select all that apply.
a \angle1
b \angle4
c \angle9
d \angle12

Question

Accepted Answer

### 11. Which pair of lines are parallel?
# Explanation:
## Step1: Recall parallel - line property
Parallel lines have equal corresponding angles.
## Step2: Analyze the given angles
We know that if two lines are cut by a transversal, corresponding angles are equal for parallel lines. Here, we see that the angles formed by lines $a$ and $c$ with the transversals have equal - measure corresponding angles. So, $a$ and $c$ are parallel.
# Answer:
B. $a$ and $c$

### 12. What is $x$?
# Explanation:
## Step1: Use the property of linear - pair
The angle adjacent to the $124^{\circ}$ angle forms a linear - pair. A linear - pair of angles sums to $180^{\circ}$. So the adjacent angle to $124^{\circ}$ is $180 - 124=56^{\circ}$.
## Step2: Use the angle - sum property of a triangle
In the triangle where $x$ is an angle, we know that the sum of the interior angles of a triangle is $180^{\circ}$. The other two angles in the triangle are $53^{\circ}$ and $39^{\circ}$. So $x = 180-(53 + 39)=88^{\circ}$.
# Answer:
$x = 88$

### 13. What is $y$?
# Explanation:
## Step1: Consider vertical angles
The angle vertical to the $42^{\circ}$ angle is also $42^{\circ}$.
## Step2: Use the angle - sum property of a triangle
In the triangle where $y$ is an angle, one angle is $42^{\circ}$ and another is $50^{\circ}$ (since the angle adjacent to $130^{\circ}$ is $50^{\circ}$). Then $y=180-(42 + 50)=88^{\circ}$.
# Answer:
C. $88$

### 14. What is $z$?
# Explanation:
## Step1: Use the property of corresponding angles
Since $a$ and $c$ are parallel, the angle corresponding to the $95^{\circ}$ angle on the other side of the transversal is also $95^{\circ}$.
## Step2: Identify $z$
$z$ is equal to this corresponding angle, so $z = 95^{\circ}$.
# Answer:
C. $95$

### 15. If the slope of line $c$ is given, the slope of which other line is known?
# Explanation:
## Step1: Recall the slope property of parallel lines
Parallel lines have the same slope. Since $a$ and $c$ are parallel, if the slope of line $c$ is given, the slope of line $a$ is the same.
# Answer:
Line $a$

### 16. What is the equation of a line that is parallel to the line $y = 2x+7$ and passes through the point $(-2,4)$?
# Explanation:
## Step1: Determine the slope of the new line
Parallel lines have the same slope. The slope of the line $y = 2x + 7$ is $m = 2$, so the slope of the new line is also $m = 2$.
## Step2: Use the point - slope form $y - y_1=m(x - x_1)$
We have $m = 2$, $x_1=-2$, and $y_1 = 4$. Substitute into the point - slope form: $y - 4=2(x+2)$.
## Step3: Simplify the equation
$$
\begin{align*}
y-4&=2x + 4\
y&=2x+8
\end{align*}
$$
# Answer:
D. $y = 2x + 8$

### 17. What is the slope of a line perpendicular to the line $y=-\frac{1}{4}x - 1$?
# Explanation:
## Step1: Recall the slope relationship of perpendicular lines
If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=-1$. Let $m_1 =-\frac{1}{4}$, then $m_2\times(-\frac{1}{4})=-1$.
## Step2: Solve for $m_2$
$$
\begin{align*}
m_2&=\frac{-1}{-\frac{1}{4}}\
m_2& = 4
\end{align*}
$$
# Answer:
$4$

### 18. Which street is parallel to 1st Ave?
# Explanation:
## Step1: Analyze the city - map grid
In a grid - like city map, parallel streets are those that run in the same direction. 2nd Ave runs in the same direction as 1st Ave.
# Answer:
A. 2nd Ave

### 19. A city road planner wants to build a road perpendicular to D Street. What is the slope of the new road?
# Explanation:
## Step1: Determine the slope of D Street
D Street has a positive slope. If we consider the grid of the city map, assume D Street has a slope $m_1$. For a line perpendicular to it, if $m_1$ is the slope of D Street, and $m_2$ is the slope of the perpendicular line, then $m_1\times m_2=-1$. If we assume D Street has a slope of $\frac{1}{1}$ (a 45 - degree angle with the axes), then the slope of the perpendicular line is $-1$.
# Answer:
$-1$

### 20. If $m\angle5=x$, which angles also have a measure of $x$?
# Explanation:
## Step1: Recall angle - relationship in parallel lines
When two parallel lines are cut by a transversal, corresponding angles are equal. $\angle5$ and $\angle9$ are corresponding angles.
# Answer:
C. $\angle9$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

11. Which pair of lines are parallel?

Step1: Recall parallel - line property

Step2: Analyze the given angles

Step1: Use the property of linear - pair

Step2: Use the angle - sum property of a triangle

Step1: Consider vertical angles

Step2: Use the angle - sum property of a triangle

Answer:

12. What is \(x\)?