Angle
Definition:
An angle is a flat geometric figure formed by two rays having the same origin. These rays are called the sides of the angle and the common point is known as the vertex of the angle.
The main characteristic of an angle is its «opening«, that is, the way in which its sides are separated.
Look at the figure of the angle:
Angle Elements:
- Sides: OA and OB
- Vertex: «O»
- Notation: Angle AOB = ∠AOB
- AOB Angle Measurement: m∠AOB
⇒ m∠AOB = α
Note:
Every time we turn an object we are turning an angle, for example: when we open a window or door, when we turn the head from left to right, or in the clock we can appreciate the angles that make the hands.
Practically the angle is in everything that surrounds us.
Measurement of an Angle
We call the measurement of an angle the measurement of the amplitude of an angle. In Geometry we will represent the angle in sexagesimal degrees (°).
To measure an angle, we use the protractor, which is an instrument with which we can easily measure angles.
With the following figure we see the steps to measure an angle with the protractor.
Step 1 – We make the vertex of the angle to be measured coincide with the center «O».
Step 2 – Identify one side of the angle, let’s see the side: OA.
Step 3 – The other side of the angle points to the protractor. We can measure any angle, Examples:
i) m∠AOB = 40°
ii) m∠AOC = 90°
iii) m∠AOD= 123°
iv) m∠AOE = 155°
Important:
In the figure we can also see other measures of angles as:
- m∠BOC = 50°
- m∠COD = 33°
- m∠BOE = 115°
In the types of angles, according to the measure, an angle can be: acute, right, obtuse.
