Acute angle

Acute angle is the Euclidean state of an angle that is less than a right angle. Its definition gives a precise comparative boundary: the angle is identified not by a particular drawing or measurement alone, but by its relation to the right angle, the standard formed when a straight line meets another straight line and the adjacent angles are equal.

Definition and Boundary

An acute angle is “an angle less than a right angle.” The wording is deliberately relational. It places the acute angle within a system of comparison in which the right angle functions as the fixed limit: any angle falling below that limit is acute, while an angle above it is obtuse.

Classification of Plane Angles

The definition gains force from its position beside the definition of the obtuse angle. The two states are presented as contrary measurements against the same reference: an obtuse angle is greater than a right angle, whereas an acute angle is less than one. This paired structure makes the right angle the dividing standard between the two classifications.

Geometrical Significance

By defining an acute angle through inequality, the text supplies a compact rule that can be applied across geometric figures. The definition does not depend on the angle's location, the lines that form it, or the figure in which it appears. What determines its status is the extent of the angle in comparison with a right angle, making the term part of the exact vocabulary required for later geometrical reasoning.