There are several different types of triangles. You can classify a triangle by its sides and its angles. There are THREE different classifications for triangles based on their sides. There are FOUR different classifications for triangles based on their angles. Types of Triangle by Angle. In an equiangular triangle, all the angles are equal—each one measures 60 degrees. An equiangular triangle is a kind of acute triangle, and is always equilateral. In a right triangle, one of the angles is a right angle—an angle of 90 degrees. A right triangle may be isosceles or scalene.