# Investigating the Geometry of Angles: Right, Acute, and Obtuse

*Angles have been integrated into many activities in our day-to-day lives, to enable precision in various functions ranging from very basic to highly complex. For navigation, construction, communication, robotics, etc. the ability to describe angles and measure them precisely is crucial. In this article, we’ll be diving into the various classifications of angles.*

## What is an angle?

An angle is the space formed at the intersection of two-line segments or the measure of rotation from one reference direction to another. They are extensively used in real-life scenarios, including:

- Directions: Terms like half-turn, full-turn, quarter-turn, and three-quarter turn are used to describe specific angles when giving directions.
- Alignment: Angles are pivotal in aligning objects with respect to a line or plane, such as positioning solar panels for maximum efficiency and adjusting the angle of a laptop screen for optimal visibility. They are also mentioned in discussions about good and bad sitting posture.
- Degree of Rotation: Describing the extent of a door’s opening, the coverage of a CCTV camera, or the specifications of a robot arm involves utilizing angles.

Angles are represented in diagrams using arcs and are measured in degrees or radians, with the protractor being the most commonly used tool for measurement.

## Classification of Angles

Angles can be classified into three main types based on their size: acute, right, and obtuse angles.

## The Right Angle

The concept of a right angle is pervasive across a wide range of applications. It represents a quarter turn or precisely an angle of 90 degrees. An illustrative example of a right angle is the corner formed where a vertical line intersects with a horizontal line. When two lines intersect to form a right angle, they are termed perpendicular lines. Unlike other angles, a right angle is denoted using a square symbol instead of an arc, as depicted in the diagram below.

We come across and utilize right angles in a lot of day-to-day activities such as:

- A camera is leveled when the vertical axis of the tripod makes a right angle with the base of the camera.
- Many conventional constructions ensure the floor and wall are perpendicular to each other.

Right angles are also used to characterize shapes. Some examples include:

- The four interior angles of a square are all right angles. Additionally, a rhombus, though having four equal sides, can be distinguished from a square by the absence of right angles in its interior angles.
- A triangle can have at most one right angle. Such a triangle is classified as a right triangle. Many geometrical properties can be derived from a right triangle, including the famous Pythagoras Theorem.

## The Acute angle

An acute angle, measuring less than 90 degrees, signifies a turn smaller than a quarter turn.

Some geometrical properties relevant to acute angles are:

- A triangle must have at least one interior angle which is an acute angle.
- A pair of acute angles that add up to 90 degrees, is known to be complementary.
- An acute triangle is a triangle that is composed of three interior angles that are all acute.

## The Obtuse Angle

If the size of an angle exceeds 90 degrees but is less than 180 degrees, then it is classified as an obtuse angle. Any turn that is greater than a quarter turn but less than a half turn is an obtuse angle.

A real-life example that depicts an obtuse angle is when we are seated for a dental procedure position the angle between our back and the seat makes an obtuse angle. Just like with acute angles and right angles, we see obtuse angles in 2d shapes as well.

- Parallelograms, rhombus, and kites have two obtuse angles amongst the four interior angles.
- A triangle can have at most one obtuse angle, and such triangles are known as obtuse triangles.
- When two non-parallel or non-perpendicular lines intersect, they form a pair of obtuse angles.