An acute angle is a type of angle that measures less than 90 degrees. That is, any angle whose measure is between 0 and 90 degrees is an acute angle without being neither a null nor a right angle.

These characteristics of acute angles imply that they always form a convex angle but can never be classified as obtuse angles. The supplementary angle of an acute angle is an obtuse angle, which are angles that measure between 90 and 180º without being straight angles.

## Examples of Acute Angles in Everyday Life

Acute angles are present in many everyday situations. Here are some examples:

Road triangles: Road triangles used to mark a disabled vehicle have three acute angles, which are used to create a stable triangular figure.

Roofs: The roofs of houses and buildings have sharp angles that are used to create the necessary slope for rainwater to run off into the drains.

Stairs: Stairs have sharp angles between the steps and the handrails, providing the necessary incline to safely ascend and descend.

Carpenter's triangles: they are instruments that have two acute angles and one right angle that are used to measure and mark wood.

Lighting: Reflectors and lights have angles less than 90 degrees that are used to focus and direct light in a specific direction.

Mirrors: Mirrors have sharp angles that are used to reflect light and create sharp images.

Art and Design: These angles are used to create a sense of depth and perspective.

## Importance of Acute Angle in Geometry

Here are some of the reasons why the acute angle is important in geometry:

### Triangles Definition

A triangle is a geometric figure consisting of three sides and three angles. The sum of the interior angles of a triangle is equal to 180 degrees. This means that at least two of the angles they form must be acute.

The angle opposite the longest side of a triangle is always acute.

In an equilateral triangle all acute angles measure 60º.

On the other hand, a right triangle is formed by a right angle and two complementary angles that are acute since it measures less than 90º. This type of triangle is also an isosceles triangle.

### Polygon Construction

A polygon is a geometric figure that consists of several sides and angles. To build regular polygons, it is necessary to use acute angles, since the sum of the interior angles of a regular polygon is a multiple of 180 degrees and each of the interior angles must be acute.

### Area Calculation

To calculate the area of geometric figures such as triangles and polygons, it is necessary to know the measure of their angles. The acute angle is one of the most important measurements for calculating the area of these figures.

### Circle Properties

In the geometry of the circle, the acute angle is used to define the central angle and the inscribed angle. The central angle is the one that forms in the center of the circle, while the inscribed angle is formed between two points on the circumference.

### Practical Applications

Geometry and an angle less than 90 have many practical applications, such as in building construction, engineering, physics, surveying, and many other areas.