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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?
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.
Free Test
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
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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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