# How I wish I'd taught... angles.

Updated: Feb 24

__What is an angle?__

An angle is defined as the measure of rotation of one line or plane relative to another, usually measured in degrees. It is formed by two rays with a common endpoint, called the vertex of the angle. An angle can also be described as the amount of turn between two lines or planes.

__Types of angles__

*Acute* -

An acute angle is an angle that measures less than 90 degrees. It is an angle that is smaller than a right angle. The name "acute" comes from the Latin word "acutus", which means "sharp" or "pointed", which describes the shape of an acute angle. An acute angle is often represented by the symbol âˆ and is measured in degrees (Â°).

*Right angle -*

A **right angle** is an angle that measures exactly 90 degrees. It is formed when two lines or segments meet at a **90-degree** angle, or when a line or segment is **perpendicular** to another. A right angle can also be described as a quarter-turn or a 90-degree rotation. The symbol for a right angle is a small square (â–) at the vertex of the angle and it is often used in geometry.

*Obtuse angle -*

An **obtuse angle** is an angle that measures **greater than 90 degrees but less than 180 degrees**. It is an angle that is larger than a right angle but smaller than a straight angle. The name "obtuse" comes from the Latin word "obtusus", which means "blunt" or "dull", describing the shape of an obtuse angle.

*Straight angle -*

A **straight angle** is an angle that measures exactly 180 degrees. It is formed when two **rays** point in exactly opposite direction . It is also referred as a "flattened" angle or "half-rotation" angle. It can be considered as the sum of two angles that are opposite rays.

*Reflex angle -*

A **reflex angle** is an angle that measures greater than 180 degrees but less than 360 degrees. It is formed when a line or segment rotates **more than a half-turn** but less **than a full turn**. The name "reflex" comes from the Latin word "reflectere" which means "to bend back" or "to turn back", describing the shape of a reflex angle. It is also known as a "concave angle"

*Full angle -*

A **full angle** is an angle that measures exactly 360 degrees. It is formed when a line or segment completes a **full rotation** or one full turn around a point. It can also be thought of as the **sum of all four right angles**. A full angle is also called a "Perigon" or "Revolution" angle. In geometry, a full angle is a way of measuring the size of an angle that goes around the whole circle.

__Common symbols.__

Lines of **equal length** are represented using a single dash. If there are two **equal sized** lines, but the set is different, then double dashes are used.

Lines that are **parallel** are shown using a single arrow. Double arrows are used to differentiate between two different pairs of **parallel** **lines**.

**Angles** that are identification are shown using a single dash through the angle or by using a pair of curved lines.

__Tri angles.__

As the name suggests, triangles have 3 angles. **Tri** meaning 3 and **angles meaning the number of verticies within the shape**. An important fact to retrieve is that of the **interior angles of a triangle** add to the sum of **180Â°**. You could model this in class using the following:

Draw a triangle using exact measurements stated by the teacher.

Mark the angles in a triangle.

Tear the angles and rearrange them to show them on a straight line, asking what the children notice.

__Angles on lines.__

Now children have **made connections** between triangles and straight lines, we may use the fact to develop a depth of thinking. Teaching children to recognise equivalent angles on lines will allow them to reason deeply about their understanding.