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 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 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 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 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.
Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the largest angle, what is the measure of the smallest angle?
A.30 degrees
B.45 degrees
C.60 degrees
D.75 degrees
Solution
Let the smallest angle be x. Then the second angle is 2x and the largest angle is 2x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (2x - 30) = 180. Solving this gives x = 30 degrees.
Q. Which of the following pairs of angles are supplementary?
A.Two acute angles
B.Two obtuse angles
C.An acute angle and an obtuse angle
D.Two right angles
Solution
Supplementary angles are two angles that add up to 180 degrees. An acute angle (less than 90 degrees) and an obtuse angle (more than 90 degrees) can add up to 180 degrees.
Correct Answer: C — An acute angle and an obtuse angle
Q. Which of the following statements is true regarding the angles formed when two lines intersect?
A.Vertical angles are always supplementary
B.Adjacent angles are always equal
C.Linear pairs are always complementary
D.Vertical angles are always equal
Solution
When two lines intersect, the angles opposite each other (vertical angles) are always equal. Therefore, the correct statement is that vertical angles are always equal.
Correct Answer: D — Vertical angles are always equal
