Can a triangle have all angles less than 60°? Give reason for your an

1.	Can a triangle have all angles less than 60°? Give reason for your answer.
Answer» No. A triangle cannot have two obtuse angles Justification: According to angle sum property, We know that the sum of all the interior angles of a triangle should be = 180°. An obtuse angle is one whose value is greater than 90° but less than 180°. Considering two angles to be equal to the lowest natural number greater than 90°, i.e., 91°. According to the question, If the triangle has two obtuse angles, then there are two angles which are at least 91° each. On adding these two angles, Sum of the two angles = 91° + 91° ⇒ Sum of the two angles = 182° The sum of these two angles already exceeds the sum of three angles of the triangle, even without considering the third angle. Therefore, a triangle cannot have two obtuse angles.

Can a triangle have all angles less than 60°? Give reason for your answer.

Answer»

No. A triangle cannot have two obtuse angles

Justification:

According to angle sum property,

We know that the sum of all the interior angles of a triangle should be = 180°.

An obtuse angle is one whose value is greater than 90° but less than 180°.

Considering two angles to be equal to the lowest natural number greater than 90°, i.e., 91°.

According to the question,

If the triangle has two obtuse angles, then there are two angles which are at least 91° each.

On adding these two angles,

Sum of the two angles = 91° + 91°

⇒ Sum of the two angles = 182°

The sum of these two angles already exceeds the sum of three angles of the triangle, even without considering the third angle.

Therefore, a triangle cannot have two obtuse angles.