Q. If angle A and angle B are supplementary, and angle A is 3 times angle B, what is the measure of angle A?
A.
90 degrees
B.
120 degrees
C.
180 degrees
D.
60 degrees
Solution
Let angle B be x. Then angle A = 3x. Since they are supplementary, x + 3x = 180, leading to 4x = 180, so x = 45. Therefore, angle A = 3 * 45 = 135 degrees.
Q. If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
A.
60 degrees
B.
80 degrees
C.
90 degrees
D.
120 degrees
Solution
Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.
Q. If the exterior angle of a triangle is 120 degrees, what is the measure of the smallest interior angle?
A.
30 degrees
B.
40 degrees
C.
60 degrees
D.
80 degrees
Solution
The exterior angle is equal to the sum of the two opposite interior angles. If the exterior angle is 120 degrees, the smallest interior angle can be calculated as 180 - 120 = 60 degrees.
Q. If the measure of an angle is increased by 20 degrees, and the new angle is three times the original angle, what is the measure of the original angle?
A.
20 degrees
B.
30 degrees
C.
40 degrees
D.
60 degrees
Solution
Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.
Q. If two angles are complementary and one angle is 10 degrees more than the other, what are the measures of the two angles?
A.
40 and 50 degrees
B.
45 and 45 degrees
C.
30 and 60 degrees
D.
35 and 55 degrees
Solution
Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 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'.
Q. In a circle, if an angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the remaining part of the circle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, it is 80/2 = 40 degrees.
Q. In a circle, if an angle subtended by an arc at the center is 80 degrees, what is the angle subtended by the same arc at any point on the circumference?
A.
20 degrees
B.
40 degrees
C.
80 degrees
D.
160 degrees
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.