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If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is?
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If one angle of a triangle is 130°. then the angle between th bisector...
Understanding the Triangle
In a triangle, the sum of all interior angles is 180°. Given one angle is 130°, we can calculate the other two angles.
Calculating the Remaining Angles
- Let the two remaining angles be A and B.
- We know: A + B + 130° = 180°
- Thus, A + B = 50°
Angle Bisectors of the Remaining Angles
The angle bisector of an angle divides it into two equal parts. Therefore:
- The bisector of angle A = A/2
- The bisector of angle B = B/2
Finding the Angle Between the Bisectors
To find the angle between the bisectors of angles A and B, we use the formula:
- Angle between two angle bisectors = 90° - (A + B)/2
Since A + B = 50°:
- Angle between the bisectors = 90° - (50°/2)
- Simplifying gives: 90° - 25° = 65°
Conclusion
Hence, the angle between the bisectors of the remaining two angles of the triangle is 65°. This result is crucial for understanding the properties of triangles and their angle bisectors, especially in competitive exams like UPSC.
In a triangle, the sum of all interior angles is 180°. Given one angle is 130°, we can calculate the other two angles.
Calculating the Remaining Angles
- Let the two remaining angles be A and B.
- We know: A + B + 130° = 180°
- Thus, A + B = 50°
Angle Bisectors of the Remaining Angles
The angle bisector of an angle divides it into two equal parts. Therefore:
- The bisector of angle A = A/2
- The bisector of angle B = B/2
Finding the Angle Between the Bisectors
To find the angle between the bisectors of angles A and B, we use the formula:
- Angle between two angle bisectors = 90° - (A + B)/2
Since A + B = 50°:
- Angle between the bisectors = 90° - (50°/2)
- Simplifying gives: 90° - 25° = 65°
Conclusion
Hence, the angle between the bisectors of the remaining two angles of the triangle is 65°. This result is crucial for understanding the properties of triangles and their angle bisectors, especially in competitive exams like UPSC.
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If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is?
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If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is?.
If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of a triangle is 130°. then the angle between th bisectors of the other 2 angles is?.
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