Q. If two lines are parallel and a transversal intersects them, what can be said about the sum of the interior angles on the same side of the transversal?
A.
They are equal to 90 degrees.
B.
They are equal to 180 degrees.
C.
They are equal to 360 degrees.
D.
They are not related.
Solution
The Interior Angles on the Same Side of the Transversal Theorem states that these angles are supplementary, meaning their sum is 180 degrees.
Correct Answer:
B
— They are equal to 180 degrees.
Q. If two lines are parallel and one line has the equation 2x + 3y = 6, what is the equation of a line parallel to it that passes through the point (1,2)?
A.
2x + 3y = 8
B.
2x + 3y = 4
C.
3x + 2y = 6
D.
3x + 2y = 8
Solution
The slope of the line 2x + 3y = 6 is -2/3. A line parallel to it will have the same slope. Using point-slope form, the equation becomes 3y - 2 = -2/3(2 - 1), which simplifies to 2x + 3y = 8.
Q. If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?
A.
y = 3x + 1
B.
y = 3x + 4
C.
y = 3x + 2
D.
y = 3x - 1
Solution
A line parallel to y = 3x + 2 will have the same slope (3). Using point-slope form, y - 4 = 3(x - 1) gives y = 3x + 1.
Q. If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1,1)?
A.
y = 3x - 2
B.
y = 3x + 1
C.
y = 3x + 3
D.
y = 3x + 0
Solution
The slope of the parallel line remains 3. Using point-slope form, y - 1 = 3(x - 1) gives y = 3x - 2.
Q. If two lines are parallel and one line has the equation y = 3x + 5, what is the equation of a line parallel to it that passes through the point (1, 2)?
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x + 3
Solution
Using the point-slope form, the equation is y - 2 = 3(x - 1), which simplifies to y = 3x - 1.
Q. If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?
A.
y = 5x - 7
B.
y = 5x + 7
C.
y = 5x + 1
D.
y = 5x - 1
Solution
A line parallel to y = 5x + 1 will have the same slope (5). Using the point-slope form: y - 3 = 5(x - 2) gives y = 5x - 7.
Q. If two lines are parallel and the angle between one line and a transversal is 40 degrees, what is the measure of the corresponding angle on the other line?
A.
40 degrees
B.
50 degrees
C.
60 degrees
D.
80 degrees
Solution
Corresponding angles are equal, so the angle on the other line is also 40 degrees.
Q. If two lines are parallel and the angle formed by one line and a transversal is 45 degrees, what is the measure of the alternate exterior angle?
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Therefore, the alternate exterior angle also measures 45 degrees.
Q. If two lines are parallel and the equation of one line is y = 3x + 5, what is the equation of a line parallel to it that passes through the point (1, 2)?
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x + 3
Solution
Using point-slope form: y - 2 = 3(x - 1) simplifies to y = 3x - 1.
Q. If two lines are parallel and the measure of one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?
A.
60 degrees
B.
90 degrees
C.
120 degrees
D.
180 degrees
Solution
Alternate exterior angles are equal when two lines are parallel. Therefore, the other alternate exterior angle also measures 120 degrees.
Q. If two lines are parallel and the measure of one of the interior angles is 45 degrees, what is the measure of the other interior angle on the same side of the transversal?
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
Solution
Interior angles on the same side of the transversal are supplementary, so 180 - 45 = 135 degrees.
Q. If two lines are parallel and the measure of one of the interior angles is 45 degrees, what is the measure of the corresponding angle on the other line?
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
Solution
Corresponding angles are equal when two lines are parallel, so the measure of the corresponding angle is also 45 degrees.
Q. If two lines are parallel and the measure of one of the interior angles is 50 degrees, what is the measure of the other interior angle on the same side of the transversal?
A.
50 degrees
B.
130 degrees
C.
180 degrees
D.
90 degrees
Solution
Interior angles on the same side of the transversal are supplementary, so 180 - 50 = 130 degrees.
