Q. If the sum of the interior angles of a quadrilateral is 360 degrees, what is the sum of the exterior angles?
A.
180 degrees
B.
360 degrees
C.
270 degrees
D.
90 degrees
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Solution
The sum of the exterior angles of any polygon is always 360 degrees.
Correct Answer:
B
— 360 degrees
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Q. If the surface area of a cube is 216 square meters, what is the length of one side of the cube?
A.
6 meters
B.
9 meters
C.
12 meters
D.
15 meters
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Solution
The surface area of a cube is given by the formula SA = 6a². Setting 6a² = 216, we find a² = 36, thus a = 6 meters.
Correct Answer:
B
— 9 meters
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Q. If the surface area of a cylinder is 150π cm² and the height is 10 cm, what is the radius?
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
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Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the surface area of a cylinder is 150π cm² and the height is 5 cm, what is the radius?
A.
5 cm
B.
3 cm
C.
4 cm
D.
2 cm
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Solution
The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(5 + r), we find r = 4 cm.
Correct Answer:
C
— 4 cm
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Q. If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the angles? (2023)
A.
40 degrees and 50 degrees
B.
45 degrees and 45 degrees
C.
35 degrees and 55 degrees
D.
30 degrees and 60 degrees
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Solution
Let the angles be x and x - 10. Then, x + (x - 10) = 90. Solving gives x = 50 degrees and the other angle is 40 degrees.
Correct Answer:
A
— 40 degrees and 50 degrees
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Q. If two angles are complementary and one angle is 10 degrees less than the other, what are the measures of the two angles?
A.
40 and 50 degrees
B.
45 and 45 degrees
C.
35 and 55 degrees
D.
30 and 60 degrees
Show solution
Solution
Let the two angles be x and x - 10. Since they are complementary, x + (x - 10) = 90. Solving gives x = 50 degrees, and the other angle is 40 degrees.
Correct Answer:
A
— 40 and 50 degrees
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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
Show solution
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.
Correct Answer:
A
— 40 and 50 degrees
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Q. If two angles are complementary and one angle is twice the other, what are the measures of the angles?
A.
30 degrees and 60 degrees
B.
20 degrees and 70 degrees
C.
45 degrees and 45 degrees
D.
10 degrees and 80 degrees
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Solution
Let the smaller angle be x. Then the larger angle is 2x. The equation x + 2x = 90 gives x = 30 degrees and 2x = 60 degrees.
Correct Answer:
A
— 30 degrees and 60 degrees
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Q. If two angles are complementary and one angle measures 25 degrees, what is the measure of the other angle?
A.
55 degrees
B.
65 degrees
C.
75 degrees
D.
85 degrees
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Solution
Complementary angles add up to 90 degrees. Therefore, the other angle is 90 - 25 = 65 degrees.
Correct Answer:
A
— 55 degrees
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Q. If two angles are complementary, what can be said about their measures?
A.
They are both greater than 90 degrees.
B.
They sum to 90 degrees.
C.
They are both less than 45 degrees.
D.
One is obtuse and the other is acute.
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Solution
Complementary angles are defined as two angles whose measures add up to 90 degrees.
Correct Answer:
B
— They sum to 90 degrees.
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Q. If two angles are complementary, what is the maximum measure of either angle?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
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Solution
Complementary angles sum to 90 degrees, so the maximum measure of either angle can be 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If two angles are complementary, what is the maximum measure of one angle if the other is 30 degrees?
A.
60 degrees
B.
90 degrees
C.
150 degrees
D.
30 degrees
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Solution
Complementary angles sum to 90 degrees. Therefore, if one angle is 30 degrees, the other must be 90 - 30 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If two angles are equal and one angle measures 45 degrees, what type of angles are they?
A.
Acute angles
B.
Obtuse angles
C.
Right angles
D.
Straight angles
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Solution
Angles measuring less than 90 degrees are classified as acute angles.
Correct Answer:
A
— Acute angles
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Q. If two angles are equal and one is 40 degrees, what is the measure of the other angle?
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
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Solution
If two angles are equal and one measures 40 degrees, the other must also measure 40 degrees.
Correct Answer:
A
— 40 degrees
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Q. If two angles are equal and one of them is 45 degrees, what type of angles are they?
A.
Acute angles
B.
Obtuse angles
C.
Right angles
D.
Straight angles
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Solution
Angles that measure less than 90 degrees are classified as acute angles. Since both angles are equal to 45 degrees, they are acute.
Correct Answer:
A
— Acute angles
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Q. If two angles are equal and their sum is 180 degrees, what type of angles are they?
A.
Acute angles
B.
Obtuse angles
C.
Right angles
D.
Straight angles
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Solution
If two angles are equal and their sum is 180 degrees, they are straight angles, each measuring 90 degrees.
Correct Answer:
D
— Straight angles
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Q. If two angles are said to be complementary, what is the maximum measure of either angle?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
180 degrees
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Solution
Complementary angles add up to 90 degrees, so the maximum measure of either angle can be 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If two angles are said to be vertically opposite, what can be inferred about their measures?
A.
They are always equal.
B.
They are always supplementary.
C.
They are always complementary.
D.
They cannot be determined.
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Solution
Vertically opposite angles are formed when two lines intersect and are always equal.
Correct Answer:
A
— They are always equal.
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Q. If two angles are said to be vertically opposite, what can be said about their measures?
A.
They are always equal.
B.
They are always supplementary.
C.
They are always complementary.
D.
They cannot be determined.
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Solution
Vertically opposite angles are formed when two lines intersect and are always equal.
Correct Answer:
A
— They are always equal.
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Q. If two angles are supplementary and one angle measures 3 times the other, what is the measure of the smaller angle? (2023)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
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Solution
Let the smaller angle be x. Then the larger angle is 3x. Since they are supplementary, x + 3x = 180. Solving gives x = 45 degrees.
Correct Answer:
A
— 30 degrees
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Q. If two circles intersect at two points, what can be said about their centers?
A.
They are the same.
B.
They are equidistant from the intersection points.
C.
They lie on the same line.
D.
They are at a fixed distance apart.
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Solution
The centers of two intersecting circles are equidistant from the points of intersection.
Correct Answer:
B
— They are equidistant from the intersection points.
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Q. If two circles intersect at two points, what can be said about their relationship?
A.
They are concentric.
B.
They are tangent to each other.
C.
They are secant to each other.
D.
They do not intersect.
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Solution
Circles that intersect at two points are said to be secant to each other.
Correct Answer:
C
— They are secant to each other.
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Q. If two circles intersect at two points, which of the following statements is true? (2021)
A.
The centers of the circles are equidistant from the intersection points.
B.
The line joining the centers of the circles passes through the intersection points.
C.
The circles are tangent to each other.
D.
The area of intersection is always a triangle.
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Solution
The centers of the circles are equidistant from the intersection points, making option 0 true.
Correct Answer:
A
— The centers of the circles are equidistant from the intersection points.
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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
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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'.
Correct Answer:
D
— All of the above
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Q. If two parallel lines are cut by a transversal, which of the following pairs of angles are equal?
A.
Alternate interior angles
B.
Corresponding angles
C.
Consecutive interior angles
D.
Both A and B
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Solution
Both alternate interior angles and corresponding angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
D
— Both A and B
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Q. If two parallel lines are cut by a transversal, which of the following statements is true? (2023)
A.
Alternate interior angles are equal
B.
Corresponding angles are supplementary
C.
Consecutive interior angles are equal
D.
All angles are acute
Show solution
Solution
When two parallel lines are cut by a transversal, alternate interior angles are equal.
Correct Answer:
A
— Alternate interior angles are equal
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Q. In a certain polygon, if each exterior angle measures 30 degrees, how many sides does the polygon have? (2023)
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Solution
The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 30 degrees, then the number of sides is 360 / 30 = 12.
Correct Answer:
A
— 6
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Q. In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?
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Solution
In a regular polygon, each interior angle can be calculated using the formula (n-2) * 180/n. Setting this equal to 120 degrees and solving for n gives n = 6, indicating a hexagon.
Correct Answer:
A
— 6
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Q. In a certain polygon, if the exterior angle is 30 degrees, how many sides does the polygon have? (2023)
Show solution
Solution
The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides n = 360 / 30 = 12.
Correct Answer:
A
— 6
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Q. In a certain polygon, the exterior angle at each vertex measures 45 degrees. How many sides does this polygon have?
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Solution
The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 45 degrees, the number of sides is 360 / 45 = 8.
Correct Answer:
C
— 8
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