Q1. If two lines are parallel and one line has an angle of 30 degrees with a transversal, what is the measure of the alternate exterior angle?
Solution:
Alternate exterior angles are equal to their corresponding angles, so the alternate exterior angle is 150 degrees.
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Q2. If the coordinates of points A and B are (2, 3) and (2, 7) respectively, what is the slope of the line segment AB?
Solution:
The slope is undefined because the x-coordinates are the same, indicating a vertical line.
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Q3. If two parallel lines are represented by the equations y = 3x + 1 and y = 3x - 4, what is the distance between them?
Solution:
The distance between two parallel lines y = mx + b1 and y = mx + b2 is |b2 - b1| / √(1 + m^2). Here, |(-4) - 1| / √(1 + 3^2) = 5 / √10 = 5/√10.
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Q4. In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the slope of the line connecting them?
Solution:
The slope is calculated as (y2 - y1) / (x2 - x1). Here, (7 - 3) / (2 - 2) is undefined because the denominator is 0.
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Q5. If angle A and angle B are alternate exterior angles formed by two parallel lines cut by a transversal, and angle A measures 120 degrees, what is the measure of angle B?
Solution:
Alternate exterior angles are equal, so angle B also measures 120 degrees.
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Q6. In a coordinate system, if line A has the equation y = -1/2x + 4 and line B is parallel to line A, what is the slope of line B?
Solution:
The slope of line B is the same as line A, which is -1/2.
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Q7. If a transversal intersects two parallel lines and creates an angle of 40 degrees, what is the measure of the vertically opposite angle?
Solution:
Vertically opposite angles are equal, so the angle is also 40 degrees.
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Q8. In a coordinate plane, if the coordinates of two points on a line are (2, 3) and (4, 7), what is the slope of the line?
Solution:
The slope is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.
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Q9. If two lines are parallel and the transversal creates an angle of 70 degrees with one of the lines, what is the measure of the corresponding angle on the other line?
Solution:
Corresponding angles are equal, so the angle on the other line is also 70 degrees.
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Q10. What is the measure of the corresponding angle if one of the angles is 75 degrees and the lines are parallel?
Solution:
Corresponding angles are equal when two parallel lines are cut by a transversal.
