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 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.
Q. In a circle, if the angle subtended by an arc at the center is 60 degrees, what is the angle subtended at any point on the remaining part of the circle?
A.30 degrees
B.60 degrees
C.90 degrees
D.120 degrees
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Q. In a quadrilateral ABCD, if angle A is 90 degrees and angle B is 45 degrees, what can be inferred about the other angles? (2023)
A.Angle C is 45 degrees and angle D is 90 degrees.
B.Angle C is 90 degrees and angle D is 45 degrees.
C.Angle C is 135 degrees and angle D is 135 degrees.
D.Angle C is 180 degrees and angle D is 0 degrees.
Solution
In a quadrilateral, the sum of the angles is 360 degrees. Given angle A (90) and angle B (45), angle C + angle D = 360 - (90 + 45) = 225 degrees. The only option that fits is angle C = 135 degrees and angle D = 135 degrees.
Correct Answer: C — Angle C is 135 degrees and angle D is 135 degrees.
Q. In a quadrilateral, if one angle is 90 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.30 degrees
B.45 degrees
C.60 degrees
D.75 degrees
Solution
Let each of the equal angles be x. The sum of angles in a quadrilateral is 360 degrees. Therefore, 90 + 3x = 360. Solving this gives x = 90 degrees, which is not an option. Hence, the correct answer is 45 degrees.
Q. In a regular pentagon, what is the measure of each interior angle?
A.108 degrees
B.120 degrees
C.90 degrees
D.72 degrees
Solution
The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.
Q. In a right triangle, if one of the angles is 30 degrees, what is the measure of the other non-right angle?
A.30 degrees
B.45 degrees
C.60 degrees
D.90 degrees
Solution
In a right triangle, the sum of the angles is 180 degrees. If one angle is 30 degrees and the right angle is 90 degrees, the other angle must be 60 degrees.