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.
Q. If two lines intersect at a point, what is the sum of the angles formed at that point?
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, but the angles formed by the intersecting lines sum up to 180 degrees.
Q. If two lines intersect, what is the sum of the angles formed at the intersection? (2021)
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.
Q. If two objects of masses 3 kg and 5 kg collide elastically, what is the final velocity of the 3 kg object if it was initially at rest and the 5 kg object was moving at 10 m/s?
A.
0 m/s
B.
3 m/s
C.
5 m/s
D.
10 m/s
Solution
Using conservation of momentum and kinetic energy, the final velocity of the 3 kg object can be calculated to be 3 m/s.
Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 45 degrees, what is the measure of the other alternate interior angle? (2020)
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other angle is also 45 degrees.
Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 75 degrees, what is the measure of the other alternate interior angle? (2020)
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate interior angle is also 75 degrees.
Q. If two parallel lines are cut by a transversal, which of the following pairs of angles are always equal?
A.
Alternate interior angles
B.
Corresponding angles
C.
Consecutive interior angles
D.
All of the above
Solution
When two parallel lines are cut by a transversal, alternate interior angles and corresponding angles are equal, while consecutive interior angles are supplementary. Therefore, the correct answer is 'All of the above'.