A triangle can have two obtuse angles
No, a triangle cannot have two obtuse angles
No, a triangle cannot have two obtuse angles.
By definition, an obtuse angle measures more than 90 degrees but less than 180 degrees. In a triangle, the sum of all three angles is always 180 degrees.
So, let’s consider the possibilities for the three angles in a triangle:
1. If a triangle has three acute angles (each measuring less than 90 degrees), then the sum of the angles would be less than 180 degrees. It cannot form a triangle.
2. If a triangle has one obtuse angle (measuring more than 90 degrees) and two acute angles, the sum of the angles would be greater than 180 degrees. It also cannot form a triangle.
3. If two angles in a triangle are obtuse, the sum of those two angles would already be more than 180 degrees. Adding a third angle, regardless of its measure, will always result in a sum greater than 180 degrees. Therefore, a triangle cannot have two obtuse angles.
In conclusion, a triangle can have at most one obtuse angle, but it cannot have two obtuse angles.
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