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The difference between supplementary and complementary angles of any given acute angle is:
- a)70°
- b)90°
- c)180°
- d)145°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The difference between supplementary and complementary angles of any g...
Concept:
Complementary angles: The pair of angles whose sum is equal to 90° are complementary angles.
Supplementary angles: The pair of angles whose sum is equal to 180° are supplementary angles.
Explanation:
Let the acute angle be a°.
⇒ Complementary angle of a° = (90 - a)°
Also, Supplementary angle of a° = (180 - a)°
∴ Difference between supplementary and complementary angles = (180 - a)° - (90 - a)°
⇒ 180 - a - 90 + a
⇒ 90°
Hence, the difference between complementary and supplementary angles of a given acute angle is 90°.
Complementary angles: The pair of angles whose sum is equal to 90° are complementary angles.
Supplementary angles: The pair of angles whose sum is equal to 180° are supplementary angles.
Explanation:
Let the acute angle be a°.
⇒ Complementary angle of a° = (90 - a)°
Also, Supplementary angle of a° = (180 - a)°
∴ Difference between supplementary and complementary angles = (180 - a)° - (90 - a)°
⇒ 180 - a - 90 + a
⇒ 90°
Hence, the difference between complementary and supplementary angles of a given acute angle is 90°.
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The difference between supplementary and complementary angles of any g...
Understanding Angles
Angles play a crucial role in geometry, particularly in understanding supplementary and complementary angles. Let's clarify what these terms mean.
Definitions
- Complementary Angles: Two angles are complementary if their measures add up to 90 degrees.
- Supplementary Angles: Two angles are supplementary if their measures add up to 180 degrees.
Given an Acute Angle
An acute angle is an angle that measures less than 90 degrees. For any acute angle 'A':
- Complement of angle A = 90 - A
- Supplement of angle A = 180 - A
Finding the Difference
To find the difference between the supplementary and complementary angles of an acute angle A, we can calculate:
1. Complementary Angle: 90 - A
2. Supplementary Angle: 180 - A
Now, we can find the difference:
Difference = (180 - A) - (90 - A)
This simplifies to:
Difference = 180 - A - 90 + A = 180 - 90 = 90 degrees.
Conclusion
Thus, the difference between the supplementary and complementary angles of any given acute angle is 90 degrees. This is why the correct answer is option 'B'. Understanding these relationships is essential for solving problems related to angles in geometry.
Angles play a crucial role in geometry, particularly in understanding supplementary and complementary angles. Let's clarify what these terms mean.
Definitions
- Complementary Angles: Two angles are complementary if their measures add up to 90 degrees.
- Supplementary Angles: Two angles are supplementary if their measures add up to 180 degrees.
Given an Acute Angle
An acute angle is an angle that measures less than 90 degrees. For any acute angle 'A':
- Complement of angle A = 90 - A
- Supplement of angle A = 180 - A
Finding the Difference
To find the difference between the supplementary and complementary angles of an acute angle A, we can calculate:
1. Complementary Angle: 90 - A
2. Supplementary Angle: 180 - A
Now, we can find the difference:
Difference = (180 - A) - (90 - A)
This simplifies to:
Difference = 180 - A - 90 + A = 180 - 90 = 90 degrees.
Conclusion
Thus, the difference between the supplementary and complementary angles of any given acute angle is 90 degrees. This is why the correct answer is option 'B'. Understanding these relationships is essential for solving problems related to angles in geometry.
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The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer?
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The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer?.
The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between supplementary and complementary angles of any given acute angle is:a)70°b)90°c)180°d)145°Correct answer is option 'B'. Can you explain this answer?.
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