Classifying angles is just giving an angle a name or type by its' measurement in degrees. There are five types of basic angles: Acute, Right, Obtuse, Straight and Reflex.
Acute Angle: an angle who has a measurement greater than 0 degrees but less than 90 degrees
Right Angle: an angle who has a measurement of exactly 90 degrees
Obtuse Angle: an angle who has a measurement greater than 90 degrees but less than 180 degrees
Straight Angle: an angle who has a measurement of exactly 180 degrees
Reflex Angle: an angle who has a measurement greater than 180 degrees but less than 360 degrees
Acute Angle: an angle who has a measurement greater than 0 degrees but less than 90 degrees
Right Angle: an angle who has a measurement of exactly 90 degrees
Obtuse Angle: an angle who has a measurement greater than 90 degrees but less than 180 degrees
Straight Angle: an angle who has a measurement of exactly 180 degrees
Reflex Angle: an angle who has a measurement greater than 180 degrees but less than 360 degrees