Q1. In a transversal intersecting two parallel lines, if one of the interior angles measures 120 degrees, what is the measure of the corresponding angle?
Solution:
Corresponding angles are equal when two parallel lines are cut by a transversal. Therefore, the corresponding angle also measures 120 degrees.
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Q2. Given two parallel lines cut by a transversal, if one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?
Solution:
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Thus, the other alternate exterior angle also measures 120 degrees.
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Q3. In a transversal intersecting two parallel lines, if one of the interior angles is 120 degrees, what is the measure of the corresponding angle?
Solution:
Corresponding angles are equal when two parallel lines are cut by a transversal. Thus, the corresponding angle also measures 120 degrees.
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Q4. In a figure with two parallel lines cut by a transversal, if one angle measures 30 degrees, what is the measure of the vertically opposite angle?
Solution:
Vertically opposite angles are equal, so the vertically opposite angle also measures 30 degrees.
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Q5. If two parallel lines are cut by a transversal and one of the same-side exterior angles is 110 degrees, what is the measure of the other same-side exterior angle?
Solution:
Same-side exterior angles are supplementary when two parallel lines are cut by a transversal. Therefore, the other angle measures 180 - 110 = 70 degrees.
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Q6. Given two parallel lines cut by a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
Solution:
Same-side interior angles are supplementary. Therefore, if one angle is 40 degrees, the other must be 180 - 40 = 140 degrees.
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Q7. If two parallel lines are cut by a transversal and one of the corresponding angles is 150 degrees, what is the measure of the other corresponding angle?
Solution:
Corresponding angles are equal when two parallel lines are cut by a transversal. Hence, the other corresponding angle also measures 150 degrees.
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Q8. If two parallel lines are cut by a transversal and one of the alternate interior angles is 55 degrees, what is the measure of the other alternate interior angle?
Solution:
By the Alternate Interior Angles Theorem, alternate interior angles are equal, so the other angle also measures 55 degrees.
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Q9. When two parallel lines are intersected by a transversal, which angles are always equal?
Solution:
Alternate interior angles are equal when two parallel lines are cut by a transversal.
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Q10. What can be concluded if two lines are cut by a transversal and the alternate interior angles are equal?
Solution:
If the alternate interior angles are equal, it can be concluded that the two lines are parallel.
