Can a triangle have two obtuse angles? give the reason for your answer

General
1

can a triangle have two obtuse angles? give the reason for your answer.

2

Can a triangle have two obtuse angles? Give the reason for your answer.

Answer: A triangle cannot have two obtuse angles. Here’s why:

1. Definition of an Obtuse Angle

  • An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

2. Sum of Angles in a Triangle

  • The sum of all internal angles in a triangle is always 180 degrees.

3. Explanation

  • If one angle in a triangle is obtuse, it is greater than 90 degrees.
  • Let’s say this angle is 91 degrees, which is the smallest possible obtuse angle.
  • This means the sum of the other two angles must be 89 degrees (because 180 - 91 = 89).
  • Each of the remaining two angles must be less than 89 degrees.
  • Therefore, both remaining angles must be acute (less than 90 degrees), as two obtuse angles would exceed 180 degrees in total.

Conclusion

  • It is impossible to have two obtuse angles in a triangle because their sum, along with any other remaining angle, would exceed 180 degrees.

Summary: A triangle cannot have two obtuse angles because the total of the angles would be more than 180 degrees, exceeding the sum required for a triangle.