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All questions of Angles for Class 6 Exam
What is an example of complementary angles?- a)30° and 60°
- b)90° and 90°
- c)120° and 60°
- d)45° and 45°
Correct answer is option 'A'. Can you explain this answer?
What is an example of complementary angles?
a)
30° and 60°
b)
90° and 90°
c)
120° and 60°
d)
45° and 45°
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Complementary angles are two angles whose measures add up to 90°. The combination of 30° and 60° is a classic example, often used in trigonometric functions and right triangles.
If angle A is 150° and angle B is 30°, what can be said about angles A and B?- a)They form a linear pair.
- b)They are vertical angles.
- c)They are supplementary.
- d)They are complementary.
Correct answer is option 'C'. Can you explain this answer?
If angle A is 150° and angle B is 30°, what can be said about angles A and B?
a)
They form a linear pair.
b)
They are vertical angles.
c)
They are supplementary.
d)
They are complementary.
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Saikat Rane answered |
Understanding Angles A and B
To analyze the relationship between angle A (150°) and angle B (30°), we can assess their definitions and properties.
Definition of Supplementary Angles
- Two angles are considered supplementary if the sum of their measures equals 180°.
- In this case, we can calculate:
- Angle A: 150°
- Angle B: 30°
- Sum: 150° + 30° = 180°
- Since the sum is equal to 180°, angles A and B are supplementary.
Other Angle Relationships
To clarify why the other options are incorrect:
- Linear Pair:
- A linear pair consists of two adjacent angles that form a straight line (sum to 180°). While angles A and B sum to 180°, they are not adjacent; hence they do not form a linear pair.
- Vertical Angles:
- Vertical angles are formed when two lines intersect, creating pairs that are opposite each other. Angles A and B are not formed in this way.
- Complementary Angles:
- Complementary angles sum to 90°. Since 150° + 30° = 180°, they do not meet this criterion.
Conclusion
Ultimately, the correct answer is option 'C': angles A and B are supplementary because their measures add up to 180°. This fundamental property of angles helps in solving many geometric problems.
To analyze the relationship between angle A (150°) and angle B (30°), we can assess their definitions and properties.
Definition of Supplementary Angles
- Two angles are considered supplementary if the sum of their measures equals 180°.
- In this case, we can calculate:
- Angle A: 150°
- Angle B: 30°
- Sum: 150° + 30° = 180°
- Since the sum is equal to 180°, angles A and B are supplementary.
Other Angle Relationships
To clarify why the other options are incorrect:
- Linear Pair:
- A linear pair consists of two adjacent angles that form a straight line (sum to 180°). While angles A and B sum to 180°, they are not adjacent; hence they do not form a linear pair.
- Vertical Angles:
- Vertical angles are formed when two lines intersect, creating pairs that are opposite each other. Angles A and B are not formed in this way.
- Complementary Angles:
- Complementary angles sum to 90°. Since 150° + 30° = 180°, they do not meet this criterion.
Conclusion
Ultimately, the correct answer is option 'C': angles A and B are supplementary because their measures add up to 180°. This fundamental property of angles helps in solving many geometric problems.
How can the length of a line segment be accurately measured?- a)By using a ruler
- b)By estimating visually
- c)By drawing an angle
- d)Using a protractor
Correct answer is option 'A'. Can you explain this answer?
How can the length of a line segment be accurately measured?
a)
By using a ruler
b)
By estimating visually
c)
By drawing an angle
d)
Using a protractor
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The length of a line segment can be accurately measured using a ruler. Placing the 0 mark at one end and aligning the ruler with the segment allows for precise measurement. This skill is fundamental in geometry and many practical applications.
If angle A measures 60° and angle B measures 30°, what type of angles are they?- a)Complementary
- b)Vertical
- c)Supplementary
- d)Adjacent
Correct answer is option 'A'. Can you explain this answer?
If angle A measures 60° and angle B measures 30°, what type of angles are they?
a)
Complementary
b)
Vertical
c)
Supplementary
d)
Adjacent
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Angles A and B are complementary because their measures add up to 90° (60° + 30° = 90°). Complementary angles are important in various geometric applications, particularly in right triangle trigonometry.
What angle measures more than 90° but less than 180°?- a)Straight Angle
- b)Right Angle
- c)Acute Angle
- d)Obtuse Angle
Correct answer is option 'D'. Can you explain this answer?
What angle measures more than 90° but less than 180°?
a)
Straight Angle
b)
Right Angle
c)
Acute Angle
d)
Obtuse Angle
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An obtuse angle measures more than 90° but less than 180°. Recognizing the characteristics of obtuse angles is useful in various geometric contexts, especially in polygon analysis.
If two angles are supplementary, what is the sum of their measures?- a)360°
- b)180°
- c)90°
- d)270°
Correct answer is option 'B'. Can you explain this answer?
If two angles are supplementary, what is the sum of their measures?
a)
360°
b)
180°
c)
90°
d)
270°
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Supplementary angles are defined as two angles whose measures add up to 180°. This relationship is crucial in solving problems involving linear pairs and other geometric configurations.
Which of the following types of angles is not a characteristic of an acute angle?- a)Measures more than 90°
- b)Measures less than 90°
- c)Common in triangles
- d)Forms a sharp corner
Correct answer is option 'B'. Can you explain this answer?
Which of the following types of angles is not a characteristic of an acute angle?
a)
Measures more than 90°
b)
Measures less than 90°
c)
Common in triangles
d)
Forms a sharp corner
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An acute angle measures less than 90°; therefore, it cannot measure more than 90°. Understanding the distinctions between different types of angles is critical in geometry.
What is the common point where the arms of an angle meet called?- a)Vertex
- b)Line
- c)Interior
- d)Arm
Correct answer is option 'A'. Can you explain this answer?
What is the common point where the arms of an angle meet called?
a)
Vertex
b)
Line
c)
Interior
d)
Arm
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The common point where the arms of an angle meet is referred to as the vertex. In geometry, the vertex serves as the point of rotation that defines the angle, and the two rays emanating from this point are known as the arms or sides of the angle.
Which type of angle measures exactly 180°?- a)Acute Angle
- b)Right Angle
- c)Obtuse Angle
- d)Straight Angle
Correct answer is option 'D'. Can you explain this answer?
Which type of angle measures exactly 180°?
a)
Acute Angle
b)
Right Angle
c)
Obtuse Angle
d)
Straight Angle
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A straight angle measures exactly 180°. It represents a straight line, which is formed when the two arms of the angle point in exactly opposite directions. This concept is essential for understanding linear relationships in geometry.
Which of the following is true about vertically opposite angles?- a)They are complementary.
- b)They are always equal.
- c)Their measures can be different.
- d)They are supplementary.
Correct answer is option 'B'. Can you explain this answer?
Which of the following is true about vertically opposite angles?
a)
They are complementary.
b)
They are always equal.
c)
Their measures can be different.
d)
They are supplementary.
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Vertically opposite angles are always equal. This property arises when two lines intersect, creating pairs of angles that share the same vertex but do not share any arms. This is a key concept in both basic geometry and more advanced mathematical studies.
What is the total sum of all angles around a point?- a)180°
- b)270°
- c)360°
- d)90°
Correct answer is option 'C'. Can you explain this answer?
What is the total sum of all angles around a point?
a)
180°
b)
270°
c)
360°
d)
90°
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The total sum of all angles around a point is always 360°. This fundamental property is crucial in various geometric calculations and helps in visualizing the complete rotation around a point.
Which of the following represents two angles that share a common arm and vertex?- a)Supplementary Angles
- b)Complementary Angles
- c)Vertically Opposite Angles
- d)Adjacent Angles
Correct answer is option 'D'. Can you explain this answer?
Which of the following represents two angles that share a common arm and vertex?
a)
Supplementary Angles
b)
Complementary Angles
c)
Vertically Opposite Angles
d)
Adjacent Angles
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Adjacent angles are defined as two angles that share a common arm and vertex, lying on opposite sides of the common arm. This relationship is important in various geometric proofs and constructions.
What type of angle is formed when two rays meet at a 90° angle?- a)Straight Angle
- b)Right Angle
- c)Acute Angle
- d)Obtuse Angle
Correct answer is option 'B'. Can you explain this answer?
What type of angle is formed when two rays meet at a 90° angle?
a)
Straight Angle
b)
Right Angle
c)
Acute Angle
d)
Obtuse Angle
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A right angle is defined as an angle that measures exactly 90°. Right angles are fundamental in geometry, particularly in defining perpendicular lines and creating right triangles.
What is the measure of a reflex angle?- a)Between 90° and 180°
- b)Exactly 360°
- c)Between 180° and 360°
- d)Less than 90°
Correct answer is option 'C'. Can you explain this answer?
What is the measure of a reflex angle?
a)
Between 90° and 180°
b)
Exactly 360°
c)
Between 180° and 360°
d)
Less than 90°
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A reflex angle measures more than 180° but less than 360°. Understanding reflex angles is important in geometry, especially when dealing with complex shapes and rotations.
In measuring angles, what does one complete rotation equal?- a)270°
- b)180°
- c)360°
- d)90°
Correct answer is option 'C'. Can you explain this answer?
In measuring angles, what does one complete rotation equal?
a)
270°
b)
180°
c)
360°
d)
90°
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One complete rotation around a point equals 360°. This property is essential for understanding angles in both geometry and practical applications like navigation and rotation in physics.
Which of the following describes an acute angle?- a)Measures exactly 90°
- b)Measures more than 0° but less than 90°
- c)Measures exactly 180°
- d)Measures more than 90° but less than 180°
Correct answer is option 'B'. Can you explain this answer?
Which of the following describes an acute angle?
a)
Measures exactly 90°
b)
Measures more than 0° but less than 90°
c)
Measures exactly 180°
d)
Measures more than 90° but less than 180°
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An acute angle is defined as an angle that measures more than 0° but less than 90°. Examples of acute angles include 15°, 30°, and 45°. Understanding the characteristics of angles helps in identifying and classifying them accurately.
What is an example of a complete angle?- a)360°
- b)90°
- c)180°
- d)45°
Correct answer is option 'A'. Can you explain this answer?
What is an example of a complete angle?
a)
360°
b)
90°
c)
180°
d)
45°
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A complete angle measures exactly 360°. This type of angle represents a full rotation and is often used in circular motion and trigonometric concepts.
What do you call angles that have the same measure?- a)Vertically Opposite Angles
- b)Adjacent Angles
- c)Complementary Angles
- d)Congruent Angles
Correct answer is option 'D'. Can you explain this answer?
What do you call angles that have the same measure?
a)
Vertically Opposite Angles
b)
Adjacent Angles
c)
Complementary Angles
d)
Congruent Angles
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Angles that have the same measure are referred to as congruent angles. This concept is significant in various geometric proofs and constructions, especially when proving triangles and other shapes are equal in measure.
Which of the following angles is considered a zero angle?- a)An angle measuring 360°
- b)An angle measuring 180°
- c)An angle that does not rotate
- d)An angle measuring 90°
Correct answer is option 'C'. Can you explain this answer?
Which of the following angles is considered a zero angle?
a)
An angle measuring 360°
b)
An angle measuring 180°
c)
An angle that does not rotate
d)
An angle measuring 90°
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A zero angle is defined as an angle where the ray does not rotate, resulting in a magnitude of 0°. This concept is often overlooked but is important for understanding the full range of angle measurements.
Which tool is typically used to measure angles?- a)Ruler
- b)Divider
- c)Compass
- d)Protractor
Correct answer is option 'D'. Can you explain this answer?
Which tool is typically used to measure angles?
a)
Ruler
b)
Divider
c)
Compass
d)
Protractor
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A protractor is the tool specifically designed for measuring angles. It typically has a semicircular scale marked from 0° to 180° and can measure angles in both clockwise and counterclockwise directions. This tool is essential in many fields, including architecture and engineering.
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