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

Question

Philoid · Accepted Answer

We know, the sum of three angles of a triangle is equal to 180°.

According to the question, if all the angles of a triangle are less than 60°, then each of the angle would be at least 59°.

⇒ Sum of the angles = 59° + 59° + 59°

⇒ Sum of the angles = 177°

⇒ The sum of the three angles of the triangle is not equal to 180°.

Similarly, for any value of the angles less than 59°, the sum of the three angles won’t be equal to 180°.

Thus, it won’t be a triangle.