No, it is not possible to have a triangle with all three angles less than 60 degrees.

In any triangle, the sum of all three interior angles is always 180 degrees.

if we assume that the three angles are A, B, and C (all less than 60 degrees), then A + B + C < 60 + 60 + 60 = 180 degrees, which is a contradiction.

Therefore, a triangle with all three angles less than 60 degrees cannot exist.