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If one angle is the average of the other two angles and the difference between the greatest and least angles
is 60°, then the formed triangle is :-
- a)An isosceles triangle
- b)An equilateral triangle
- c)A right angled triangle
- d)A right angled isosceles triangle
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If one angle is the average of the other two angles and the difference...
Let's call the three angles A, B, and C.
We know that the average of two angles is equal to the third angle, so we can set up the equation:
(A + B)/2 = C
We also know that the difference between the greatest and least angles is 60, so we can set up another equation:
C - A = 60
We can solve these equations simultaneously to find the values of A, B, and C.
From the first equation, we have:
A + B = 2C
Substituting this into the second equation, we get:
2C - A = 60
Rearranging this equation, we have:
A = 2C - 60
Substituting this value of A back into the first equation, we have:
(2C - 60) + B = 2C
Simplifying this equation, we get:
B = 60
So, the middle angle B is 60 degrees.
From the first equation, we have:
A + 60 = 2C
Substituting this into the second equation, we get:
2C - A = 60
Substituting the value of A from the first equation, we have:
2C - (2C - 60) = 60
Simplifying this equation, we get:
60 = 60
This equation is true, which means that the values of A, B, and C can be any numbers that satisfy the given conditions.
Therefore, we cannot determine the exact values of A, B, and C without additional information.
We know that the average of two angles is equal to the third angle, so we can set up the equation:
(A + B)/2 = C
We also know that the difference between the greatest and least angles is 60, so we can set up another equation:
C - A = 60
We can solve these equations simultaneously to find the values of A, B, and C.
From the first equation, we have:
A + B = 2C
Substituting this into the second equation, we get:
2C - A = 60
Rearranging this equation, we have:
A = 2C - 60
Substituting this value of A back into the first equation, we have:
(2C - 60) + B = 2C
Simplifying this equation, we get:
B = 60
So, the middle angle B is 60 degrees.
From the first equation, we have:
A + 60 = 2C
Substituting this into the second equation, we get:
2C - A = 60
Substituting the value of A from the first equation, we have:
2C - (2C - 60) = 60
Simplifying this equation, we get:
60 = 60
This equation is true, which means that the values of A, B, and C can be any numbers that satisfy the given conditions.
Therefore, we cannot determine the exact values of A, B, and C without additional information.
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Community Answer
If one angle is the average of the other two angles and the difference...
C
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If one angle is the average of the other two angles and the difference between the greatest and least anglesis 60°, then the formed triangle is :-a)An isosceles triangleb)An equilateral trianglec)A right angled triangled)A right angled isosceles triangleCorrect answer is option 'C'. Can you explain this answer?
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If one angle is the average of the other two angles and the difference between the greatest and least anglesis 60°, then the formed triangle is :-a)An isosceles triangleb)An equilateral trianglec)A right angled triangled)A right angled isosceles triangleCorrect answer is option 'C'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If one angle is the average of the other two angles and the difference between the greatest and least anglesis 60°, then the formed triangle is :-a)An isosceles triangleb)An equilateral trianglec)A right angled triangled)A right angled isosceles triangleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one angle is the average of the other two angles and the difference between the greatest and least anglesis 60°, then the formed triangle is :-a)An isosceles triangleb)An equilateral trianglec)A right angled triangled)A right angled isosceles triangleCorrect answer is option 'C'. Can you explain this answer?.
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