Q. If angle A and angle B are alternate exterior angles formed by a transversal intersecting two parallel lines, and angle A measures 120 degrees, what is the measure of angle B?
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Solution
Alternate exterior angles are equal when a transversal intersects parallel lines. Therefore, angle B also measures 120 degrees.
Q. If angle A and angle B are alternate exterior angles formed by a transversal intersecting two parallel lines, what can be concluded about their measures?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
Solution
By the Alternate Exterior Angles Theorem, alternate exterior angles are equal when formed by a transversal intersecting two parallel lines.
Q. If angle A and angle B are same-side interior angles formed by a transversal intersecting two parallel lines, and angle A measures 65 degrees, what is the measure of angle B?
A.
115 degrees
B.
65 degrees
C.
180 degrees
D.
90 degrees
Solution
Same-side interior angles are supplementary. Therefore, angle B = 180 - 65 = 115 degrees.
Q. If angle C is 30 degrees and is an interior angle on the same side of the transversal as angle D, what is the measure of angle D if the lines are parallel?
A.
30 degrees
B.
150 degrees
C.
90 degrees
D.
180 degrees
Solution
Since angle C and angle D are interior angles on the same side of the transversal, they are supplementary. Therefore, angle D = 180 - 30 = 150 degrees.
Q. If angle C is 30 degrees and is one of the corresponding angles formed by a transversal intersecting two parallel lines, what is the measure of the other corresponding angle?
A.
30 degrees
B.
150 degrees
C.
90 degrees
D.
60 degrees
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the other corresponding angle also measures 30 degrees.
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 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 parallel lines are cut by a transversal and one of the alternate interior angles is 120 degrees, what is the measure of the other alternate interior angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Solution
By the Alternate Interior Angles Theorem, alternate interior angles are equal. Thus, the other alternate interior angle also measures 120 degrees.
Q. If two parallel lines are cut by a transversal and one of the angles formed is 150 degrees, what is the measure of the alternate interior angle?
A.
30 degrees
B.
150 degrees
C.
180 degrees
D.
90 degrees
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the alternate interior angle measures 30 degrees (180 - 150).
Q. In a diagram with two parallel lines and a transversal, if one of the interior angles is 40 degrees, what is the measure of the corresponding angle?
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the corresponding angle also measures 40 degrees.
Q. In a pair of parallel lines cut by a transversal, if one of the interior angles is 120 degrees, what is the measure of the corresponding exterior angle?
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Solution
The corresponding exterior angle is supplementary to the interior angle. Therefore, it measures 180 - 120 = 60 degrees.
Q. In a pair of parallel lines cut by a transversal, if one of the interior angles is 55 degrees, what is the measure of the corresponding exterior angle?
A.
125 degrees
B.
55 degrees
C.
180 degrees
D.
90 degrees
Solution
The corresponding exterior angle is supplementary to the interior angle. Thus, it measures 180 - 55 = 125 degrees.
