Q. In a quadrilateral, if one angle is 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
40 degrees
C.
60 degrees
D.
80 degrees
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Solution
The sum of angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. Dividing this by 3 gives 80 degrees for each of the equal angles.
Correct Answer:
C
— 60 degrees
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Q. In a quadrilateral, if one angle is 120 degrees, what can be said about the sum of the other three angles?
A.
They must sum to 60 degrees.
B.
They must sum to 180 degrees.
C.
They must sum to 240 degrees.
D.
They must sum to 360 degrees.
Show solution
Solution
The sum of the angles in a quadrilateral is 360 degrees. Therefore, the other three angles must sum to 360 - 120 = 240 degrees.
Correct Answer:
C
— They must sum to 240 degrees.
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Q. In a quadrilateral, if one angle is 90 degrees and the opposite angle is 90 degrees, what can be concluded about the quadrilateral?
A.
It is a rectangle.
B.
It is a square.
C.
It is a parallelogram.
D.
It is a trapezium.
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Solution
If a quadrilateral has two opposite angles of 90 degrees, it must be a rectangle.
Correct Answer:
A
— It is a rectangle.
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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
Show solution
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.
Correct Answer:
B
— 45 degrees
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Q. In a quadrilateral, if the lengths of all sides are equal, which of the following is true?
A.
It is a rectangle.
B.
It is a rhombus.
C.
It is a square.
D.
It can be any quadrilateral.
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Solution
If all sides of a quadrilateral are equal, it is a rhombus, but it can also be a square if the angles are right.
Correct Answer:
B
— It is a rhombus.
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Q. In a quadrilateral, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
It can only be a rectangle.
B.
It can be a triangle.
C.
It can be any four-sided figure.
D.
It can only be a square.
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Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which applies to all four-sided figures.
Correct Answer:
C
— It can be any four-sided figure.
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Q. In a quadrilateral, if three angles are 70 degrees, 80 degrees, and 90 degrees, what is the measure of the fourth angle?
A.
120 degrees
B.
100 degrees
C.
110 degrees
D.
130 degrees
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Solution
The sum of the angles in a quadrilateral is 360 degrees. Thus, the fourth angle is 360 - (70 + 80 + 90) = 120 degrees.
Correct Answer:
B
— 100 degrees
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Q. In a rectangle, which of the following is true about the diagonals? (2023)
A.
They are perpendicular.
B.
They are equal and bisect each other.
C.
They are unequal.
D.
They do not bisect each other.
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Solution
In a rectangle, the diagonals are equal in length and bisect each other.
Correct Answer:
B
— They are equal and bisect each other.
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Q. In a regular dodecagon, what is the measure of each exterior angle?
A.
30 degrees
B.
36 degrees
C.
24 degrees
D.
18 degrees
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Solution
The measure of each exterior angle of a regular polygon is 360/n. For a dodecagon (n=12), it is 360/12 = 30 degrees.
Correct Answer:
B
— 36 degrees
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Q. In a regular hexagon, what is the measure of each interior angle?
A.
120 degrees
B.
90 degrees
C.
150 degrees
D.
60 degrees
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Solution
The measure of each interior angle in a regular hexagon can be calculated using the formula (n-2) * 180/n, which gives (6-2) * 180/6 = 120 degrees.
Correct Answer:
A
— 120 degrees
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Q. In a regular hexagon, what is the relationship between the side length and the radius of the circumscribed circle?
A.
The radius is twice the side length.
B.
The radius is equal to the side length.
C.
The radius is half the side length.
D.
The radius is three times the side length.
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Solution
In a regular hexagon, the radius of the circumscribed circle is equal to the length of a side.
Correct Answer:
B
— The radius is equal to the side length.
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Q. In a regular pentagon, what is the measure of each exterior angle? (2023)
A.
60 degrees
B.
72 degrees
C.
90 degrees
D.
108 degrees
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Solution
The measure of each exterior angle in a regular polygon is 360/n. For a pentagon (n=5), it is 360/5 = 72 degrees.
Correct Answer:
B
— 72 degrees
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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
Show solution
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.
Correct Answer:
A
— 108 degrees
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Q. In a regular pentagon, what is the relationship between the number of sides and the number of diagonals? (2023)
A.
Diagonals are equal to sides.
B.
Diagonals are twice the number of sides.
C.
Diagonals are three times the number of sides.
D.
Diagonals are less than the number of sides.
Show solution
Solution
In a regular pentagon, the number of diagonals is given by n(n-3)/2. For n=5, it results in 5(5-3)/2 = 5, which is equal to the number of sides.
Correct Answer:
A
— Diagonals are equal to sides.
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Q. In a regular polygon, if the measure of each exterior angle is 30 degrees, how many sides does the polygon have? (2023)
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Solution
The measure of each exterior angle of a regular polygon is given by 360/n. Setting 360/n = 30 gives n = 12.
Correct Answer:
A
— 6
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Q. In a rhombus, what can be said about the angles?
A.
All angles are equal
B.
Opposite angles are equal
C.
Adjacent angles are equal
D.
All angles are right angles
Show solution
Solution
In a rhombus, opposite angles are equal.
Correct Answer:
B
— Opposite angles are equal
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Q. In a rhombus, what can be said about the diagonals?
A.
They are equal and bisect each other at right angles.
B.
They are unequal and bisect each other at right angles.
C.
They are equal and do not bisect each other.
D.
They are unequal and do not bisect each other.
Show solution
Solution
In a rhombus, the diagonals are unequal and bisect each other at right angles.
Correct Answer:
B
— They are unequal and bisect each other at right angles.
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Q. In a rhombus, what is the relationship between the lengths of the diagonals?
A.
They are equal
B.
They are perpendicular
C.
They bisect the angles
D.
Both B and C
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Solution
In a rhombus, the diagonals are perpendicular and they bisect the angles.
Correct Answer:
D
— Both B and C
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Q. In a right triangle, if one angle measures 30 degrees, what is the measure of the other non-right angle?
A.
60 degrees
B.
30 degrees
C.
90 degrees
D.
45 degrees
Show solution
Solution
In a right triangle, the sum of the angles is 180 degrees. Therefore, the other angle must be 180 - 90 - 30 = 60 degrees.
Correct Answer:
A
— 60 degrees
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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
Show solution
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.
Correct Answer:
C
— 60 degrees
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Q. In a right triangle, if one of the non-right angles is 30 degrees, what is the measure of the other non-right angle?
A.
60 degrees
B.
30 degrees
C.
90 degrees
D.
45 degrees
Show solution
Solution
In a right triangle, the sum of the angles is 180 degrees. Therefore, the other angle is 90 - 30 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. In a right triangle, if one of the non-right angles is 45 degrees, what is the measure of the other non-right angle?
A.
45 degrees
B.
60 degrees
C.
30 degrees
D.
90 degrees
Show solution
Solution
In a right triangle, the sum of the angles is 180 degrees. Therefore, the other non-right angle must also be 45 degrees.
Correct Answer:
A
— 45 degrees
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Q. In a square, if the length of one side is doubled, what happens to the area of the square?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It increases by 50%
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Solution
If the side length of a square is doubled, the area increases by a factor of four (since area = side^2).
Correct Answer:
C
— It quadruples
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Q. In a trapezium, which of the following statements is true?
A.
All sides are equal.
B.
Only one pair of opposite sides is parallel.
C.
Both pairs of opposite sides are parallel.
D.
It has four right angles.
Show solution
Solution
In a trapezium, only one pair of opposite sides is parallel.
Correct Answer:
B
— Only one pair of opposite sides is parallel.
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Q. In a triangle formed by the points A(1, 2), B(4, 6), and C(1, 6), which of the following statements is true?
A.
AB is parallel to AC
B.
AB is perpendicular to AC
C.
AC is longer than AB
D.
All sides are equal
Show solution
Solution
The slope of AB is (6-2)/(4-1) = 4/3, and the slope of AC is (6-2)/(1-1) which is undefined. Since one slope is undefined, AB is perpendicular to AC.
Correct Answer:
B
— AB is perpendicular to AC
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Q. In a triangle, if one angle is 90 degrees, what can be inferred about the other two angles?
A.
They are both acute angles.
B.
One is obtuse and the other is acute.
C.
They are both obtuse angles.
D.
They are equal.
Show solution
Solution
In a right triangle, the sum of the other two angles must be 90 degrees, making them both acute.
Correct Answer:
A
— They are both acute angles.
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Q. In a triangle, if one angle is twice the size of another angle, and the third angle is 30 degrees less than the first angle, what is the measure of the smallest angle?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let the smallest angle be x. Then the second angle is 2x and the third angle is x - 30. The sum of angles in a triangle is 180 degrees. Therefore, x + 2x + (x - 30) = 180. Solving this gives x = 30 degrees.
Correct Answer:
A
— 30 degrees
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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
Show solution
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.
Correct Answer:
A
— 30 degrees
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Q. In a triangle, if one angle is twice the size of another angle, what is the measure of the smallest angle? (2023)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
Let the smallest angle be x. Then the second angle is 2x, and the third angle is 180 - 3x. Solving gives x = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a triangle, if one angle measures 45 degrees and the other measures 45 degrees, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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