An angle that has a measure of less than 90°: Tommy's father was visiting at his son's kindergarten and had to sit on one of the little chairs with his legs bent at an an acute angle.

An angle that has a measure of more than 90° and less than 180°: Tom's teacher said that the angle between a person's nose and forehead is an obtuse angle.

He also asked his students to bend their arms in an obtuse angle.

The angle between the direction of interest (of the Sun, for example) and the zenith (directly overhead): The zenith angle is the angle between the direction to the zenith (point of the celestial sphere vertically overhead) and the direction of a light ray.