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In a parallelogram, how are the consecutive angles related?
- a)They are equal
- b)They are complementary
- c)They are obtuse
- d)They are supplementary
Correct answer is option 'D'. Can you explain this answer?
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In a parallelogram, how are the consecutive angles related?a)They are ...
In a parallelogram, consecutive angles are supplementary, meaning they add up to 180 degrees. This relationship arises from the parallel nature of opposite sides and is instrumental in solving various geometric problems involving parallelograms.
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In a parallelogram, how are the consecutive angles related?a)They are ...
Understanding Consecutive Angles in a Parallelogram
In a parallelogram, the relationship between consecutive angles is quite specific and can be understood through the properties of the shape.
Definition of a Parallelogram
- A parallelogram is a quadrilateral with opposite sides that are both equal and parallel.
- The opposite angles are also equal, which is a key property of the shape.
Angles in a Parallelogram
- Let’s denote the angles of a parallelogram as A, B, C, and D.
- In a parallelogram, angles A and B are consecutive angles. Similarly, angles C and D are also consecutive.
Relationship of Consecutive Angles
- The consecutive angles in a parallelogram are supplementary.
- This means that each pair of consecutive angles adds up to 180 degrees.
Why Are They Supplementary?
- Since opposite angles are equal (Angle A = Angle C and Angle B = Angle D), this leads to the following:
- Angle A + Angle B = 180 degrees
- Angle C + Angle D = 180 degrees
- This property is a direct result of the parallel nature of the opposite sides, which causes the interior angles to interact in a way that they sum to 180 degrees.
Conclusion
Thus, the correct answer is option 'D': The consecutive angles in a parallelogram are supplementary. This property is fundamental in understanding the nature of parallelograms and is essential for solving problems related to their angles.
In a parallelogram, the relationship between consecutive angles is quite specific and can be understood through the properties of the shape.
Definition of a Parallelogram
- A parallelogram is a quadrilateral with opposite sides that are both equal and parallel.
- The opposite angles are also equal, which is a key property of the shape.
Angles in a Parallelogram
- Let’s denote the angles of a parallelogram as A, B, C, and D.
- In a parallelogram, angles A and B are consecutive angles. Similarly, angles C and D are also consecutive.
Relationship of Consecutive Angles
- The consecutive angles in a parallelogram are supplementary.
- This means that each pair of consecutive angles adds up to 180 degrees.
Why Are They Supplementary?
- Since opposite angles are equal (Angle A = Angle C and Angle B = Angle D), this leads to the following:
- Angle A + Angle B = 180 degrees
- Angle C + Angle D = 180 degrees
- This property is a direct result of the parallel nature of the opposite sides, which causes the interior angles to interact in a way that they sum to 180 degrees.
Conclusion
Thus, the correct answer is option 'D': The consecutive angles in a parallelogram are supplementary. This property is fundamental in understanding the nature of parallelograms and is essential for solving problems related to their angles.
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In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer?.
In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a parallelogram, how are the consecutive angles related?a)They are equalb)They are complementaryc)They are obtused)They are supplementaryCorrect answer is option 'D'. Can you explain this answer?.
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