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If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the option
a) 50°,
b)155°
c)145°
d)135°?
a) 50°,
b)155°
c)145°
d)135°?
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If one angle of a trianlge is 130 °, then find the angle between the b...
Understanding the Triangle's Angles
To find the angle between the bisectors of the other two angles of a triangle, we first need to establish the angles of the triangle.
- Given angle A = 130°.
- The sum of angles in a triangle = 180°.
- Therefore, angles B + C = 180° - 130° = 50°.
Finding Angles B and C
Let’s denote:
- Angle B = x
- Angle C = 50° - x
Angle Bisectors
The angle bisectors of angles B and C divide them into two equal parts:
- Angle bisector of B = x/2
- Angle bisector of C = (50° - x)/2
Calculating the Angle Between Bisectors
The angle between the two angle bisectors can be calculated using the formula:
Angle between bisectors = 90° + (A/2)
Substituting the given value:
- A = 130°
Thus,
Angle between bisectors = 90° + (130°/2)
Calculating this gives:
- Angle between bisectors = 90° + 65° = 155°.
Conclusion
The angle between the bisectors of the other two angles is:
- 155°.
So, the correct answer from the options provided is b) 155°.
To find the angle between the bisectors of the other two angles of a triangle, we first need to establish the angles of the triangle.
- Given angle A = 130°.
- The sum of angles in a triangle = 180°.
- Therefore, angles B + C = 180° - 130° = 50°.
Finding Angles B and C
Let’s denote:
- Angle B = x
- Angle C = 50° - x
Angle Bisectors
The angle bisectors of angles B and C divide them into two equal parts:
- Angle bisector of B = x/2
- Angle bisector of C = (50° - x)/2
Calculating the Angle Between Bisectors
The angle between the two angle bisectors can be calculated using the formula:
Angle between bisectors = 90° + (A/2)
Substituting the given value:
- A = 130°
Thus,
Angle between bisectors = 90° + (130°/2)
Calculating this gives:
- Angle between bisectors = 90° + 65° = 155°.
Conclusion
The angle between the bisectors of the other two angles is:
- 155°.
So, the correct answer from the options provided is b) 155°.
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If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°?
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If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°? 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 trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°?.
If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°? 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 trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle of a trianlge is 130 °, then find the angle between the bisectors of the other two angle from the optiona) 50°,b)155°c)145°d)135°?.
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