# Acute angle

## Definition

An angle of less than $90^\circ$ is called an acute angle

The meaning of acute is, an angle of less than $90^\circ$. Therefore, if any angle is less than $90^\circ$, the angle is called as an acute angle geometrically.

Zero angle is a best example of an acute angle because the range of acute angle starts from zero degrees and ends just before $90^\circ$.

Mathematically, the range of an acute angle can be expressed as $[0^\circ, 90^\circ)$.

### Case study

Acute angles are geometrically formed in two different possible cases.

Angle of any line is measured from the zero degrees because it is parallel to the surface of the earth.

$\overrightarrow{AB}$ is a ray and it is initially at $0^\circ$ angle. Later, the ray $\overrightarrow{AB}$ is rotated an angle of $56^\circ$ in anticlockwise direction to become $\overrightarrow{AC}$ at its final position.

The ray $\overrightarrow{AB}$ is made an angle of $56^\circ$ to reach its final position from its initial position.

$\angle CAB = 56^\circ$

The angle $CAB$ is less than $90^\circ$. Therefore, the $\angle CAB$ is called as an acute angle.

2

#### Acute angle between two lines

$\overrightarrow{DE}$ and $\overrightarrow{DF}$ are two rays and they both started from point $D$.

The two rays have a common vertex and an angle is formed between them. The angle between them is measured by considering one ray as baseline to measure the angle of another ray and vice-versa.

The angle between them is measured as $38^\circ$.

$\angle EDF = 38^\circ$

The angle $EDF$ is less than $90^\circ$. Therefore, it is called as an acute angle geometrically.