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If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles is
- a)65°
- b)115°
- c)130°
- d)155°
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If one angle of a triangle is 130°, then the angle between the bis...
Understanding the Triangle's Angles
In a triangle, the sum of all angles is always 180 degrees. Given that one angle is 130 degrees, we can find the other two angles.
Calculating the Remaining Angles
- Let the two remaining angles be A and B.
- A + B + 130 = 180
- Therefore, A + B = 50 degrees.
Identifying the Angle Bisectors
- The angle bisector of an angle divides it into two equal parts.
- Thus, the bisectors of angles A and B will create two new angles: A/2 and B/2.
Finding the Angle Between the Bisectors
- The angle between the bisectors of angles A and B can be determined using the formula:
Angle between the bisectors = 90 - (A + B)/2
- Substituting A + B = 50 into the formula:
Angle = 90 - (50)/2
Angle = 90 - 25
Angle = 65 degrees.
Correction in Approach
- The angle calculated above is incorrect when considering the triangle's configuration.
- The correct approach involves understanding the exterior angles formed by the bisectors when the triangle is extended.
Final Calculation
- The angle between the bisectors is actually given by:
Angle = 180 - (A + B)/2
- Therefore:
Angle = 180 - 25 = 155 degrees.
Conclusion
Thus, the angle between the bisectors of the other two angles in the triangle is 155 degrees, confirming that the correct answer is option 'D'.
In a triangle, the sum of all angles is always 180 degrees. Given that one angle is 130 degrees, we can find the other two angles.
Calculating the Remaining Angles
- Let the two remaining angles be A and B.
- A + B + 130 = 180
- Therefore, A + B = 50 degrees.
Identifying the Angle Bisectors
- The angle bisector of an angle divides it into two equal parts.
- Thus, the bisectors of angles A and B will create two new angles: A/2 and B/2.
Finding the Angle Between the Bisectors
- The angle between the bisectors of angles A and B can be determined using the formula:
Angle between the bisectors = 90 - (A + B)/2
- Substituting A + B = 50 into the formula:
Angle = 90 - (50)/2
Angle = 90 - 25
Angle = 65 degrees.
Correction in Approach
- The angle calculated above is incorrect when considering the triangle's configuration.
- The correct approach involves understanding the exterior angles formed by the bisectors when the triangle is extended.
Final Calculation
- The angle between the bisectors is actually given by:
Angle = 180 - (A + B)/2
- Therefore:
Angle = 180 - 25 = 155 degrees.
Conclusion
Thus, the angle between the bisectors of the other two angles in the triangle is 155 degrees, confirming that the correct answer is option 'D'.
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If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer?
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If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 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 the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer?.
If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 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 the bisectors of the other two angles isa)65°b)115°c)130°d)155°Correct answer is option 'D'. Can you explain this answer?.
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