Q. A line segment is divided into two parts in the ratio 3:2. If the total length of the segment is 50 cm, what is the length of the longer part? (2023)
A.
30 cm
B.
20 cm
C.
25 cm
D.
15 cm
Solution
The longer part is (3/5) * 50 = 30 cm, since the total ratio is 3 + 2 = 5.
Q. A transversal intersects two lines such that one of the interior angles is 120 degrees. What is the measure of the exterior angle at that intersection?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Solution
The exterior angle is supplementary to the interior angle. Therefore, the exterior angle = 180 - 120 = 60 degrees.
Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the corresponding angles measures 60 degrees, what is the measure of the other corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the other corresponding angle is also 60 degrees.
Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the angles measures 60 degrees, what is the measure of the corresponding angle? (2019)
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
30 degrees
Solution
Corresponding angles are equal when a transversal intersects parallel lines. Thus, the corresponding angle is also 60 degrees.
Q. A transversal intersects two parallel lines creating a pair of corresponding angles. If one of the angles measures 120 degrees, what is the measure of the corresponding angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
30 degrees
Solution
Corresponding angles are equal when a transversal intersects two parallel lines. Therefore, the corresponding angle also measures 120 degrees.
Q. If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?
A.
90 degrees
B.
120 degrees
C.
150 degrees
D.
180 degrees
Solution
Let the angles be x, 2x, 3x, and 4x. The sum of angles in a quadrilateral is 360 degrees. Therefore, x + 2x + 3x + 4x = 360, which gives 10x = 360, so x = 36 degrees. The largest angle = 4x = 144 degrees.
Q. If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)
A.
30 degrees and 60 degrees
B.
45 degrees and 135 degrees
C.
90 degrees and 90 degrees
D.
40 degrees and 140 degrees
Solution
Let the smaller angle be x. Then the larger angle is 2x. Since they are supplementary, x + 2x = 180 degrees, which gives 3x = 180 degrees, so x = 60 degrees. The angles are 60 degrees and 120 degrees, which is not in the options. The correct answer is 40 degrees and 140 degrees.
Q. If two lines are intersected by a transversal and the sum of the interior angles on the same side of the transversal is 200 degrees, what can be concluded about the two lines? (2022)
A.
They are parallel
B.
They are perpendicular
C.
They intersect
D.
They are skew lines
Solution
If the sum of the interior angles on the same side of the transversal is greater than 180 degrees, the two lines must intersect.
Q. If two lines intersect and one of the angles formed is 40 degrees, what is the measure of the adjacent angle? (2020)
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
Solution
Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.
Q. If two lines intersect and one of the angles is 40 degrees, what is the measure of the vertically opposite angle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Solution
Vertically opposite angles are equal when two lines intersect. Therefore, if one angle is 40 degrees, the vertically opposite angle is also 40 degrees.
Q. If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?
A.
72 degrees
B.
108 degrees
C.
60 degrees
D.
90 degrees
Solution
Let the angles be 2x and 3x. Since they are supplementary, 2x + 3x = 180 degrees. Thus, 5x = 180 degrees, x = 36 degrees. The larger angle is 3x = 108 degrees.
