6. two parallel lines are cut by a transversal. a pair of same - side interior angles formed have measures of (2x - 11)° and (9x + 6.75)°. what is the measure of the smaller angle? 7. what are the values of x and y? a x = 30; y = 76 b x = 76; y = 48 c x = 80; y = 54 d x = 132; y = 48 8. two parallel lines are cut by a transversal. what kind of angle pair are angles 1 and 2? a alternate interior angles b alternate exterior angles c same - side exterior angles d corresponding angles spiral review 9. if a unit circle with a center at (-3, 4) is reflected across the x - axis, where will the center of the reflected image lie? 10. one triangle has angles that measure 45° and 83°. another triangle has angles that measure 45° and 52°. are the triangles similar? how do you know? 11. an office manager is planning to set up three computer workstations and a printer in a space that is 22 feet wide. the printer takes up 4 feet. a. write an equation that you could use to find the width w (in feet) of the space available for each computer work station. b. what is the width of the space available for each computer work station?

Question

Accepted Answer

### 6.
# Explanation:
## Step1: Recall same - side interior angles property
Same - side interior angles formed by two parallel lines and a transversal are supplementary, so $(2x - 11)+(9x + 6.75)=180$.
## Step2: Combine like terms
$2x+9x-11 + 6.75=180$, which simplifies to $11x-4.25 = 180$.
## Step3: Isolate the variable term
Add 4.25 to both sides: $11x=180 + 4.25=184.25$.
## Step4: Solve for x
Divide both sides by 11: $x=\frac{184.25}{11}=16.75$.
## Step5: Find the measures of the angles
Substitute $x = 16.75$ into the angle expressions. The first angle is $2x-11=2	imes16.75-11=33.5 - 11 = 22.5^{\circ}$, and the second angle is $9x + 6.75=9	imes16.75+6.75=150.75+6.75 = 157.5^{\circ}$. The smaller angle is $22.5^{\circ}$.
# Answer:
$22.5^{\circ}$

### 7.
We assume that the angles are related by angle - properties of parallel lines and transversals. The $132^{\circ}$ angle and the angle adjacent to $y^{\circ}$ are supplementary (linear - pair).
# Explanation:
## Step1: Find the value of y
The angle adjacent to the $132^{\circ}$ angle is $180 - 132=48^{\circ}$. Since this angle and $y^{\circ}$ are vertical angles, $y = 48$.
## Step2: Find the value of x
The $56^{\circ}$ angle and $x^{\circ}$ are related such that the sum of the angles in the triangle - like part formed by the parallel lines and transversal gives us the relationship. The third angle in the triangle - like part (with angles $56^{\circ}$ and $y = 48^{\circ}$) and $x^{\circ}$ are supplementary. First, find the third angle in the triangle: $180-(56 + 48)=76^{\circ}$. Then, since this angle and $x^{\circ}$ are supplementary, $x=76$.
# Answer:
B. $x = 76;y = 48$

### 8.
# Brief Explanations:
By the definition of alternate interior angles, when two parallel lines are cut by a transversal, alternate interior angles are non - adjacent angles that lie between the two parallel lines and on opposite sides of the transversal. Angles 1 and 2 fit this description.
# Answer:
A. alternate interior angles

### 9.
# Explanation:
## Step1: Recall the rule for reflecting a point across the x - axis
The rule for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$.
## Step2: Apply the rule to the center of the circle
The center of the unit circle is $(-3,4)$. When reflected across the x - axis, the x - coordinate remains the same and the y - coordinate changes sign. So the new center is $(-3,-4)$.
# Answer:
$(-3,-4)$

### 10.
# Explanation:
## Step1: Find the third angle of the first triangle
The sum of the interior angles of a triangle is $180^{\circ}$. For the first triangle with angles $45^{\circ}$ and $83^{\circ}$, the third angle is $180-(45 + 83)=52^{\circ}$.
## Step2: Compare the angles of the two triangles
The first triangle has angles $45^{\circ},83^{\circ},52^{\circ}$ and the second triangle has angles $45^{\circ},52^{\circ}$. Since two pairs of corresponding angles are equal (the $45^{\circ}$ and $52^{\circ}$ angles), by the AA (angle - angle) similarity criterion, the two triangles are similar.
# Answer:
Yes, because two pairs of corresponding angles are equal.

### 11.
A.
# Explanation:
## Step1: Set up the equation
The total width of the space is 22 feet. The printer takes up 4 feet, and there are 3 computer workstations of width w each. So the equation is $3w+4 = 22$.
# Answer:
$3w + 4=22$

B.
# Explanation:
## Step1: Solve the equation for w
Starting with $3w+4 = 22$, subtract 4 from both sides: $3w=22 - 4=18$.
## Step2: Isolate w
Divide both sides by 3: $w=\frac{18}{3}=6$.
# Answer:
6 feet

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QUESTION IMAGE

Question

Explanation:

6.

Step1: Recall same - side interior angles property

Step2: Combine like terms

Step3: Isolate the variable term

Step4: Solve for x

Step5: Find the measures of the angles

Step1: Find the value of y

Step2: Find the value of x

Answer:

7.