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 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, 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. In a triangle, if one angle is 45 degrees and the other is 45 degrees, what is the measure of the third angle? (2020)
A.90 degrees
B.45 degrees
C.60 degrees
D.30 degrees
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.
Q. Two lines are perpendicular to each other. If one line makes an angle of 30 degrees with the horizontal, what is the angle made by the other line with the horizontal? (2022)
A.30 degrees
B.60 degrees
C.90 degrees
D.120 degrees
Solution
If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.
Q. Two parallel lines are cut by a transversal. If one of the alternate interior angles is 65 degrees, what is the measure of the other alternate interior angle? (2020)
A.65 degrees
B.115 degrees
C.180 degrees
D.75 degrees
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.
Q. What is the measure of each angle in a regular hexagon? (2019)
A.120 degrees
B.90 degrees
C.60 degrees
D.150 degrees
Solution
The measure of each interior angle in a regular hexagon can be calculated using the formula (n-2) * 180/n, where n is the number of sides. For a hexagon, n=6, so the measure is (6-2) * 180/6 = 120 degrees.
Q. What is the relationship between the sum of the interior angles of a triangle and the angles formed by a transversal cutting through two parallel lines? (2022)
A.They are equal
B.They are supplementary
C.They are complementary
D.They are unrelated
Solution
The sum of the interior angles of a triangle is 180 degrees, and the angles formed by a transversal cutting through two parallel lines are supplementary, meaning they add up to 180 degrees.
