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If one angle of the triangle is equal to the sum of the other two angles then the triangle is
- a)Acute angled triangle
- b)Isosceles/ equilateral triangle
- c)Obtuse angled triangle
- d)Right angled triangle
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If one angle of the triangle is equal to the sum of the other two angl...
Answer:
Explanation:
In a triangle, the sum of all angles is always 180 degrees. Let's assume the three angles of the triangle are A, B, and C.
Given:
One angle (let's assume A) is equal to the sum of the other two angles (B and C).
To prove:
The triangle is a right-angled triangle.
Proof:
Let's assume that angle A is equal to the sum of angles B and C.
So, A = B + C
Now, let's assume that the triangle is not a right-angled triangle. In this case, the sum of angles B and C would be less than 90 degrees (acute-angled triangle) or greater than 90 degrees (obtuse-angled triangle).
Case 1: Acute-angled triangle
If the sum of angles B and C is less than 90 degrees, it means that angle A (which is equal to B + C) would also be less than 90 degrees. However, this contradicts the given condition that angle A is equal to the sum of angles B and C. Therefore, an acute-angled triangle cannot satisfy the given condition.
Case 2: Obtuse-angled triangle
If the sum of angles B and C is greater than 90 degrees, it means that angle A (which is equal to B + C) would also be greater than 90 degrees. However, this again contradicts the given condition that angle A is equal to the sum of angles B and C. Therefore, an obtuse-angled triangle cannot satisfy the given condition.
Hence, the only possibility left is that the triangle is a right-angled triangle, where the sum of angles B and C is equal to 90 degrees. In this case, angle A (which is equal to B + C) would also be equal to 90 degrees.
Therefore, the correct answer is option 'D' - Right-angled triangle.
Explanation:
In a triangle, the sum of all angles is always 180 degrees. Let's assume the three angles of the triangle are A, B, and C.
Given:
One angle (let's assume A) is equal to the sum of the other two angles (B and C).
To prove:
The triangle is a right-angled triangle.
Proof:
Let's assume that angle A is equal to the sum of angles B and C.
So, A = B + C
Now, let's assume that the triangle is not a right-angled triangle. In this case, the sum of angles B and C would be less than 90 degrees (acute-angled triangle) or greater than 90 degrees (obtuse-angled triangle).
Case 1: Acute-angled triangle
If the sum of angles B and C is less than 90 degrees, it means that angle A (which is equal to B + C) would also be less than 90 degrees. However, this contradicts the given condition that angle A is equal to the sum of angles B and C. Therefore, an acute-angled triangle cannot satisfy the given condition.
Case 2: Obtuse-angled triangle
If the sum of angles B and C is greater than 90 degrees, it means that angle A (which is equal to B + C) would also be greater than 90 degrees. However, this again contradicts the given condition that angle A is equal to the sum of angles B and C. Therefore, an obtuse-angled triangle cannot satisfy the given condition.
Hence, the only possibility left is that the triangle is a right-angled triangle, where the sum of angles B and C is equal to 90 degrees. In this case, angle A (which is equal to B + C) would also be equal to 90 degrees.
Therefore, the correct answer is option 'D' - Right-angled triangle.
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Community Answer
If one angle of the triangle is equal to the sum of the other two angl...
Let the angles of triangle be x, y and
180° - ( x + y).
∴ 180° - (x + y) = (x + y)
⇒ 2(x + y) = 180°
⇒ x + y = 90°
∴ (180°- (x + y)) = 180° - 90° = 90°
∴ The triangle will be right angled triangle
180° - ( x + y).
∴ 180° - (x + y) = (x + y)
⇒ 2(x + y) = 180°
⇒ x + y = 90°
∴ (180°- (x + y)) = 180° - 90° = 90°
∴ The triangle will be right angled triangle
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If one angle of the triangle is equal to the sum of the other two angles then the triangle isa)Acute angled triangleb)Isosceles/ equilateral triangle c)Obtuse angled triangled)Right angled triangleCorrect answer is option 'D'. Can you explain this answer?
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