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The bisectors of any two adjacent angles of a parallelogram intersect at
- a)30°
- b)45°
- c)60°
- d)90°
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The bisectors of any two adjacent angles of a parallelogram intersect ...
The Angle Properties of a Parallelogram
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to 180°).
Understanding the Angles
Let’s denote the angles of a parallelogram as A, B, C, and D. Then, we have:
- Angle A = Angle C
- Angle B = Angle D
- A + B = 180°
The Bisectors of Adjacent Angles
Now, consider two adjacent angles, say Angle A and Angle B. Their measures can be expressed as:
- A + B = 180°
When we draw the bisectors of these angles, they divide each angle into two equal parts:
- Angle A is divided into A/2 and A/2
- Angle B is divided into B/2 and B/2
Finding the Measure of the Angle Between the Bisectors
The angle between the two bisectors can be calculated as follows:
- Angle between bisectors = (A/2) + (B/2)
Substituting B = 180° - A, we get:
- Angle between bisectors = (A/2) + ((180° - A)/2)
This simplifies to:
- Angle between bisectors = (A + 180° - A)/2 = 180°/2 = 90°
Conclusion
Thus, the angle formed by the intersection of the bisectors of any two adjacent angles of a parallelogram is always 90°. Therefore, the correct answer is option 'D' - 90°.
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to 180°).
Understanding the Angles
Let’s denote the angles of a parallelogram as A, B, C, and D. Then, we have:
- Angle A = Angle C
- Angle B = Angle D
- A + B = 180°
The Bisectors of Adjacent Angles
Now, consider two adjacent angles, say Angle A and Angle B. Their measures can be expressed as:
- A + B = 180°
When we draw the bisectors of these angles, they divide each angle into two equal parts:
- Angle A is divided into A/2 and A/2
- Angle B is divided into B/2 and B/2
Finding the Measure of the Angle Between the Bisectors
The angle between the two bisectors can be calculated as follows:
- Angle between bisectors = (A/2) + (B/2)
Substituting B = 180° - A, we get:
- Angle between bisectors = (A/2) + ((180° - A)/2)
This simplifies to:
- Angle between bisectors = (A + 180° - A)/2 = 180°/2 = 90°
Conclusion
Thus, the angle formed by the intersection of the bisectors of any two adjacent angles of a parallelogram is always 90°. Therefore, the correct answer is option 'D' - 90°.
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The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct 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 The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct 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 The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct answer is option 'D'. Can you explain this answer?.
The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct 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 The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct 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 The bisectors of any two adjacent angles of a parallelogram intersect ata)30°b)45°c)60°d)90°Correct answer is option 'D'. Can you explain this answer?.
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