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If one angle is the average of the other two angles and the difference between the greatest and the least angles is 60 degrees, then the formed triangle is called
- 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...
Given conditions:
- One angle is the average of the other two angles.
- The difference between the greatest and the least angles is 60 degrees.
To determine the type of triangle formed, let's consider the three angles of the triangle.
Let the three angles of the triangle be A, B, and C, where C is the angle that is the average of the other two angles.
1. Average Angle:
C = (A + B) / 2
2. Difference between Angles:
The difference between the greatest and the least angles is 60 degrees.
Therefore, we can write:
A - B = 60
Now, let's analyze the options:
a) An isosceles triangle:
In an isosceles triangle, two angles are equal. However, there is no information given that suggests that any two angles are equal. Hence, option 'a' is not correct.
b) An equilateral triangle:
In an equilateral triangle, all three angles are equal. Again, there is no information given that suggests that all three angles are equal. Therefore, option 'b' is not correct.
d) A right-angled isosceles triangle:
In a right-angled isosceles triangle, two angles are equal and one angle is a right angle (90 degrees). There is no information given that suggests that any angle is a right angle. Thus, option 'd' is not correct.
c) A right-angled triangle:
In a right-angled triangle, one angle is a right angle (90 degrees). Since there is no information given about any angle being a right angle, we cannot conclude that the formed triangle is a right-angled triangle. Therefore, option 'c' is not correct.
Since all of the given options are incorrect, we can conclude that none of the options accurately describe the type of triangle formed with the given conditions.
- One angle is the average of the other two angles.
- The difference between the greatest and the least angles is 60 degrees.
To determine the type of triangle formed, let's consider the three angles of the triangle.
Let the three angles of the triangle be A, B, and C, where C is the angle that is the average of the other two angles.
1. Average Angle:
C = (A + B) / 2
2. Difference between Angles:
The difference between the greatest and the least angles is 60 degrees.
Therefore, we can write:
A - B = 60
Now, let's analyze the options:
a) An isosceles triangle:
In an isosceles triangle, two angles are equal. However, there is no information given that suggests that any two angles are equal. Hence, option 'a' is not correct.
b) An equilateral triangle:
In an equilateral triangle, all three angles are equal. Again, there is no information given that suggests that all three angles are equal. Therefore, option 'b' is not correct.
d) A right-angled isosceles triangle:
In a right-angled isosceles triangle, two angles are equal and one angle is a right angle (90 degrees). There is no information given that suggests that any angle is a right angle. Thus, option 'd' is not correct.
c) A right-angled triangle:
In a right-angled triangle, one angle is a right angle (90 degrees). Since there is no information given about any angle being a right angle, we cannot conclude that the formed triangle is a right-angled triangle. Therefore, option 'c' is not correct.
Since all of the given options are incorrect, we can conclude that none of the options accurately describe the type of triangle formed with the given conditions.
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Community Answer
If one angle is the average of the other two angles and the difference...
If one angle is the average of the other two angles and the difference between the greatest and the least angles is 60 degrees, then the formed triangle is called a right-angled triangle. The angles will be 90 degrees, 60 degrees, 30 degrees.
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If one angle is the average of the other two angles and the difference between the greatest and the least angles is 60 degrees, then the formed triangle is calleda)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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