Q1. Two parallel lines are cut by a transversal, creating angles of 75° and x°. What is the value of x?
Solution:
The angles are supplementary, so x = 180° - 75° = 105°.
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Q2. If angle 1 and angle 2 are alternate exterior angles formed by a transversal intersecting two parallel lines, what is true about their measures?
Solution:
Alternate exterior angles are equal when two parallel lines are cut by a transversal.
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Q3. In a transversal intersecting two parallel lines, if one angle measures 55°, what is the measure of the adjacent angle?
Solution:
Adjacent angles formed by a transversal are supplementary, so the adjacent angle is 180° - 55° = 125°.
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Q4. In a pair of parallel lines cut by a transversal, if one of the interior angles is 120°, what is the measure of the corresponding angle?
Solution:
Corresponding angles are equal, so the corresponding angle is also 120°.
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Q5. If angle 1 and angle 2 are alternate interior angles and angle 1 measures 55°, what is the measure of angle 2?
Solution:
Alternate interior angles are equal, so angle 2 also measures 55°.
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Q6. What is the sum of the measures of the interior angles formed by two parallel lines and a transversal?
Solution:
The sum of the measures of all interior angles formed by a transversal cutting two parallel lines is 360°.
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Q7. In a pair of parallel lines cut by a transversal, if one of the interior angles is 120°, what is the measure of the other interior angle on the same side of the transversal?
Solution:
The two interior angles on the same side of the transversal are supplementary, so the other angle is 180° - 120° = 60°.
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Q8. What is the sum of the interior angles formed by two parallel lines and a transversal?
Solution:
The sum of the interior angles formed by two parallel lines and a transversal is 360°.
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Q9. If two parallel lines are cut by a transversal and one of the angles is 45°, what is the measure of the angle that is supplementary to it?
Solution:
Supplementary angles add up to 180°, so the angle that is supplementary to 45° is 180° - 45° = 135°.
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Q10. If two lines are parallel and a transversal creates an angle of 40°, what is the measure of the alternate exterior angle?
Solution:
The alternate exterior angle is equal to the angle formed by the transversal, so it is 40°.
