1. A skateboard ramp has a 158º entry angle. Find the measure of ∠1.
A.) 22º
B.) 68º
C.) 78º
D.) 58º
2. Which of the following equations parallel to the line passing through A(-2, 7);B(-2, -2)?
A.) y = -2
B.) y = x
C.) 3x = 5
D.) -2x = 7y
3. Which of the following equations would graph a line parallel to 3y = 2x - x + 5?
A.) 3y = x + 1
B.) y = x + 1
C.) y = 2/3x + 1
D.) 3/2y = x + 1
Answers are 100%
1. Option B. (Parallel lines with a line crossed through it.)
2. C. - x=14, y=12
3. C. - Alternate exterior angles
4. C. - A line perpendicular to a given line through a point not on the line.
5. B. - 18
6. B. - m<1=m<8
7. B. - 68 degrees
8. C. - <2 and <7
9. (Short essay) Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. This means that angle 1 = angle 5. If r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6. Angle 1 = angle 5, so r and s are parallel.
10. (short essay) 1. <1 and <5 are supplementary. 1. Given 2. Vertical angles are congruent 3. Substitution. 4. L || M 4. Consecutive Interior Angles Theorem.
11. (Short Essay) B is wrong because they are not supplementary. They a alternate interior angels so they are equal.
12. (Short Essay)
X=81 Z=99 Y=68
I assume it's 22.
AB is vertical. Which equation is a vertical line?
I suspect a typo (2x-x), but as written, the slope is 1/3. Which of the choices has slope 1/3?
1. To find the measure of ∠1, we need to use the fact that the sum of the angles in a triangle is 180º.
Since the entry angle is 158º, the sum of ∠1 and the right angle (∠2) is 180º - 158º = 22º.
Therefore, the measure of ∠1 is 22º.
The correct answer is A.) 22º.
2. To find an equation parallel to the line passing through points A(-2, 7) and B(-2, -2), we need to find the slope of this line.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by (y₂ - y₁) / (x₂ - x₁).
Using the given points A(-2, 7) and B(-2, -2), we get (7 - (-2)) / (-2 - (-2)) = 9 / 0.
Note that the denominator of 0 indicates that the line is vertical and parallel to the y-axis.
Therefore, the equation of a line parallel to this line is of the form x = k, where k is any constant.
Among the options, the equation x = -2 is parallel to the given line.
The correct answer is A.) x = -2.
3. To find an equation parallel to the line given by 3y = 2x - x + 5, we need to find the slope of this line.
In the given equation, the slope is the coefficient of x when the equation is written in slope-intercept form (y = mx + b).
Rewriting the equation 3y = 2x - x + 5 as y = (2/3)x + 5/3, we can see that the slope is 2/3.
Since parallel lines have equal slopes, an equation parallel to the given line should also have a slope of 2/3.
Among the options, the equation y = (2/3)x + 1 has a slope of 2/3 and is parallel to the given line.
The correct answer is C.) y = (2/3)x + 1.
1. To find the measure of ∠1, we need to know that the sum of angles around a point is 360º.
∠1 is the angle between the entry angle of the skateboard ramp (158º) and the horizontal line.
To find ∠1, subtract 158º from 360º:
360º - 158º = 202º
Therefore, the measure of ∠1 is 202º.
Answer: There is no option provided in the given answer choices, so none of them is correct.
2. To determine which equation is parallel to the line passing through A(-2, 7) and B(-2, -2), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope.
First, calculate the slope (m) of the line passing through points A and B using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the given coordinates:
m = (-2 - 7) / (-2 - (-2))
m = -9 / 0
m is undefined.
Since the slope is undefined, the line is vertical.
Answer: None of the options provided in the answer choices is parallel to a vertical line, so none of them is correct.
3. To determine which equation would graph a line parallel to 3y = 2x - x + 5, we need to find the slope of the given equation.
The given equation is in the form 3y = 2x - x + 5. Simplify it to:
3y = x + 5
Now, rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = (1/3)x + 5/3
The slope of this line is (1/3).
To have a parallel line, the slope needs to be the same.
Checking the answer choices, the equation that has the same slope of (1/3) is:
C.) y = 2/3x + 1
Therefore, the equation y = 2/3x + 1 would graph a line parallel to 3y = 2x - x + 5.
Answer: C.) y = 2/3x + 1