Greatest Angle in a Triangle

Our adopted textbook, Holt Geometry, has the following definitions:

"Acute triangle is a triangle with three acute angles."

"Obtuse triangle is a triangle with one obtuse angle."

"Right triangle is a triangle with one right angle."

Using the triangle sum theorem, one would see that there can only be one right angle or one obtuse angle in any triangle.

In my class, I don't see any problem if my students would come up with the following definitions:

Acute triangle is a triangle whose greatest angle is acute.

Obtuse triangle is a triangle whose greatest angle is obtuse.

Right triangle is a triangle whose greatest angle is right.


And what do you think of this take on equiangular triangle:

"Equiangular triangle is a triangle whose greatest angle is 60 degrees"?