Class 7 Exam > Class 7 Questions > Which of the following statements is false?a)...
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Which of the following statements is false?
- a)Two vertically opposite angles can be acute
- b)Two vertically opposite angles can be obtuse
- c)Two vertically opposite angles can be right angles
- d)Two vertically opposite angles may be unequal
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which of the following statements is false?a)Two vertically opposite a...
- Vertically opposite angles are formed when two lines intersect.
- These angles are always equal to each other.
- Options A, B, and C are true because vertically opposite angles can be both acute, obtuse, or right angles, as long as they are equal.
- Option D is false because vertically opposite angles are always equal.
- Therefore, statement D is incorrect.
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Which of the following statements is false?a)Two vertically opposite a...
Understanding Vertically Opposite Angles
When two lines intersect, they create pairs of angles known as vertically opposite angles. These angles are formed across from each other and possess unique properties.
Properties of Vertically Opposite Angles
- Vertically opposite angles are always equal. This means if one angle measures, say, 30 degrees, the angle directly opposite it will also measure 30 degrees.
- Since they are equal, they can all be classified as:
- Acute angles (less than 90 degrees)
- Obtuse angles (greater than 90 degrees but less than 180 degrees)
- Right angles (exactly 90 degrees)
Analyzing the Statements
Let's evaluate the statements:
- Statement A: Two vertically opposite angles can be acute.
- This is true; both angles can measure less than 90 degrees.
- Statement B: Two vertically opposite angles can be obtuse.
- This is true; both angles can measure more than 90 degrees but less than 180 degrees.
- Statement C: Two vertically opposite angles can be right angles.
- This is true; both angles can measure exactly 90 degrees.
- Statement D: Two vertically opposite angles may be unequal.
- This is false; by definition, vertically opposite angles are always equal.
Conclusion
Thus, the correct answer is option 'D' because it contradicts the fundamental property of vertically opposite angles, which states they must be equal in measure.
When two lines intersect, they create pairs of angles known as vertically opposite angles. These angles are formed across from each other and possess unique properties.
Properties of Vertically Opposite Angles
- Vertically opposite angles are always equal. This means if one angle measures, say, 30 degrees, the angle directly opposite it will also measure 30 degrees.
- Since they are equal, they can all be classified as:
- Acute angles (less than 90 degrees)
- Obtuse angles (greater than 90 degrees but less than 180 degrees)
- Right angles (exactly 90 degrees)
Analyzing the Statements
Let's evaluate the statements:
- Statement A: Two vertically opposite angles can be acute.
- This is true; both angles can measure less than 90 degrees.
- Statement B: Two vertically opposite angles can be obtuse.
- This is true; both angles can measure more than 90 degrees but less than 180 degrees.
- Statement C: Two vertically opposite angles can be right angles.
- This is true; both angles can measure exactly 90 degrees.
- Statement D: Two vertically opposite angles may be unequal.
- This is false; by definition, vertically opposite angles are always equal.
Conclusion
Thus, the correct answer is option 'D' because it contradicts the fundamental property of vertically opposite angles, which states they must be equal in measure.
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Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer?.
Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is false?a)Two vertically opposite angles can be acuteb)Two vertically opposite angles can be obtusec)Two vertically opposite angles can be right anglesd)Two vertically opposite angles may be unequalCorrect answer is option 'D'. Can you explain this answer?.
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