# Angle

## Angle

A geometric figure formed by two rays that have the same endpoint.

• The point where the two rays meet is called the vertex of the angle.
• The angle formed by the two rays can be measured using a protractor.
• The context generally indicates the type of measurement system used to measure an angle.
• The measure of an angle in a plane is always a positive number. However, an angle of rotation can be positive or negative

### Symbols

The angle shown below can be named in two ways:

• ∠1 is read as “angle 1.”
• ∠BAC is read as “angle BAC.”

The measure of angle 1 can be written as “m∠1.” .

The notation “∠A,” which is read as “angle A,” is often used to refer to an angle with the vertex A. However, using the vertex (a point) to refer to an angle or its measure inevitably leads to confusion, given that there are two angles at the vertex. The example below shows a reflex angle and an acute angle.

In a diagram, an angle is usually indicated by a small arc of a circle at the vertex of the angle. A right angle is indicated by a small square at the vertex.

### Examples

• The notation “m∠BAC = 40° ” is read as “the measure of angle BAC is equal to 40 degrees.”

• The notation “m$$∠$$α = $$\frac{\pi}{4}$$” is read as “the measure of angle a is equal to $$\frac{\pi}{4}$$ “.