Q. In a circle, if a central angle measures 80 degrees, what is the measure of the inscribed angle that subtends the same arc?
A.
20 degrees
B.
40 degrees
C.
80 degrees
D.
160 degrees
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Solution
The inscribed angle is half the measure of the central angle that subtends the same arc. Therefore, the inscribed angle measures 80/2 = 40 degrees.
Correct Answer:
B
— 40 degrees
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Q. In a circle, if a chord is drawn, which of the following statements is true regarding the angles formed?
A.
The angles subtended by the chord at the center are equal.
B.
The angles subtended by the chord at the circumference are equal.
C.
The angles subtended at the center are half of those at the circumference.
D.
The angles subtended at the circumference are equal to those at the center.
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Solution
The angles subtended by the same chord at the circumference are equal.
Correct Answer:
B
— The angles subtended by the chord at the circumference are equal.
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Q. In a circle, if a chord is perpendicular to a radius at its endpoint, what can be inferred about the chord?
A.
It is the longest chord.
B.
It bisects the circle.
C.
It is a diameter.
D.
It is bisected by the radius.
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Solution
A radius that is perpendicular to a chord at its endpoint bisects the chord.
Correct Answer:
D
— It is bisected by the radius.
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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
Show solution
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.
Correct Answer:
B
— 40 degrees
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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 remaining part of the circle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Show solution
Solution
The angle subtended at the circumference is half the angle subtended at the center. Therefore, it is 80/2 = 40 degrees.
Correct Answer:
A
— 40 degrees
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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 circumference?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Correct Answer:
A
— 30 degrees
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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
Show solution
Solution
The angle subtended at the circumference is half of that at the center, so it is 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In a circle, if the length of an arc is 10 cm and the radius is 5 cm, what is the angle in radians subtended by the arc at the center? (2021)
A.
1 rad
B.
2 rad
C.
3 rad
D.
4 rad
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Solution
The angle in radians is given by the formula θ = s/r, where s is the arc length. Thus, θ = 10/5 = 2 rad.
Correct Answer:
B
— 2 rad
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Q. In a circle, if the radius is doubled, how does the area change?
A.
It remains the same.
B.
It doubles.
C.
It quadruples.
D.
It increases by a factor of eight.
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Solution
If the radius is doubled, the area increases by a factor of four (since area is proportional to the square of the radius).
Correct Answer:
C
— It quadruples.
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Q. In a circle, if the radius is increased by 50%, what happens to the area of the circle?
A.
It increases by 50%
B.
It doubles
C.
It increases by 125%
D.
It increases by 75%
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Solution
If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.
Correct Answer:
C
— It increases by 125%
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Q. In a circle, if the radius is increased by 50%, what happens to the area?
A.
Increases by 25%
B.
Increases by 50%
C.
Increases by 75%
D.
Increases by 125%
Show solution
Solution
If the radius increases by 50%, the new radius is 1.5r. The area becomes π(1.5r)² = 2.25πr², which is an increase of 125%.
Correct Answer:
D
— Increases by 125%
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Q. In a coordinate plane, if the point A(2, 3) is reflected across the x-axis, what are the coordinates of the reflected point?
A.
(2, -3)
B.
(3, 2)
C.
(-2, 3)
D.
(3, -2)
Show solution
Solution
Reflecting a point across the x-axis changes the sign of the y-coordinate. Thus, A(2, 3) becomes (2, -3).
Correct Answer:
A
— (2, -3)
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Q. In a coordinate plane, if the point A(2, 3) is reflected over the x-axis, what are the coordinates of the reflected point?
A.
(2, -3)
B.
(3, 2)
C.
(-2, 3)
D.
(-3, -2)
Show solution
Solution
Reflecting a point (x, y) over the x-axis results in (x, -y). Therefore, A(2, 3) becomes (2, -3).
Correct Answer:
A
— (2, -3)
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Q. In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possible measure of the opposite angle?
A.
100 degrees
B.
80 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, if one angle is 80 degrees, the opposite angle can be 100 degrees.
Correct Answer:
A
— 100 degrees
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Q. In a cyclic quadrilateral, the opposite angles are related in which of the following ways?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are independent.
Show solution
Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
B
— They are supplementary.
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Q. In a cyclic quadrilateral, the opposite angles are related in which way? (2023)
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are independent.
Show solution
Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
B
— They are supplementary.
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Q. In a cyclic quadrilateral, which of the following is true regarding its opposite angles?
A.
They are equal.
B.
They are supplementary.
C.
They are complementary.
D.
They are congruent.
Show solution
Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
B
— They are supplementary.
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Q. In a cyclic quadrilateral, which of the following is true?
A.
The opposite angles are supplementary
B.
All sides are equal
C.
The diagonals are equal
D.
It has at least one right angle
Show solution
Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
A
— The opposite angles are supplementary
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Q. In a cyclic quadrilateral, which of the following properties holds true?
A.
The sum of opposite angles is 180 degrees.
B.
All sides are equal.
C.
It has at least one right angle.
D.
The diagonals are equal.
Show solution
Solution
In a cyclic quadrilateral, the sum of opposite angles is always 180 degrees.
Correct Answer:
A
— The sum of opposite angles is 180 degrees.
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Q. In a cyclic quadrilateral, which of the following statements is true?
A.
The opposite angles are supplementary.
B.
All sides are equal.
C.
It has at least one right angle.
D.
It can only be a square.
Show solution
Solution
In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.
Correct Answer:
A
— The opposite angles are supplementary.
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Q. In a parallelogram, if one angle measures 60 degrees, what is the measure of the opposite angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
In a parallelogram, opposite angles are equal, so the opposite angle also measures 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. In a parallelogram, if the base is 12 cm and the height is 5 cm, what is the area? (2020)
A.
60 cm²
B.
70 cm²
C.
80 cm²
D.
90 cm²
Show solution
Solution
Area of a parallelogram = base * height = 12 * 5 = 60 cm².
Correct Answer:
A
— 60 cm²
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Q. In a parallelogram, which of the following properties holds true?
A.
All sides are equal.
B.
Diagonals bisect each other.
C.
All angles are right angles.
D.
Only opposite angles are equal.
Show solution
Solution
In a parallelogram, the diagonals bisect each other, which is a defining property of parallelograms.
Correct Answer:
B
— Diagonals bisect each other.
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Q. In a parallelogram, which of the following properties is NOT true?
A.
Opposite angles are equal.
B.
Adjacent angles are supplementary.
C.
All sides are equal.
D.
Diagonals bisect each other.
Show solution
Solution
In a parallelogram, while opposite angles are equal and diagonals bisect each other, all sides being equal is a property of a rhombus, not all parallelograms.
Correct Answer:
C
— All sides are equal.
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Q. In a polygon, if the sum of the interior angles is 720 degrees, how many sides does the polygon have? (2023)
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Solution
The formula for the sum of the interior angles of a polygon is (n-2) * 180, where n is the number of sides. Setting (n-2) * 180 = 720 gives n = 6.
Correct Answer:
B
— 6
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Q. In a quadrilateral ABCD, if AB = CD and AD = BC, which of the following can be concluded?
A.
ABCD is a rectangle.
B.
ABCD is a parallelogram.
C.
ABCD is a trapezium.
D.
ABCD is a square.
Show solution
Solution
If both pairs of opposite sides are equal, then ABCD is a parallelogram.
Correct Answer:
B
— ABCD is a parallelogram.
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about the sum of angles C and D?
A.
C and D must be 100 degrees
B.
C and D must be 180 degrees
C.
C and D must be 90 degrees
D.
C and D must be 360 degrees
Show solution
Solution
The sum of the angles in any quadrilateral is 360 degrees. Given angles A and B, we can find C + D = 360 - (70 + 110) = 180 degrees.
Correct Answer:
B
— C and D must be 180 degrees
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Q. In a quadrilateral ABCD, if angle A is 70 degrees and angle B is 110 degrees, what can be inferred about angles C and D?
A.
They must be equal.
B.
They must be supplementary.
C.
They can be any values.
D.
They must be complementary.
Show solution
Solution
The sum of the angles in a quadrilateral is 360 degrees. Therefore, angles C and D must sum to 180 degrees, making them supplementary.
Correct Answer:
B
— They must be supplementary.
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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.
Show solution
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.
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Q. In a quadrilateral ABCD, if the sum of the interior angles is 360 degrees, which of the following statements is true?
A.
ABCD is a rectangle.
B.
ABCD can be any shape.
C.
ABCD must be a square.
D.
ABCD is a triangle.
Show solution
Solution
The sum of the interior angles of any quadrilateral is always 360 degrees, which means ABCD can be any shape that satisfies this condition.
Correct Answer:
B
— ABCD can be any shape.
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