Angles

Angles

Introduction

An angle is a figure formed by two rays. The side of the angle sharing a common starting point called the vertex of the angle. An angle is made of three main points.

How to represent angles

we represent angles with a symbol “∠”  and we use the 3 points’ names to name the angle.

Remember: the vertex of the angle’s point name should always be in the middle of the name. like below…
∠AOB or ∠BOA

Names of angles

• acute angle
• right angle
• obtuse angle
• straight angle
• reflex angle
• full rotation

degrees

Before we learn more about angles we are going to learn a unit of measurement called degrees.
Degrees are a unit of measurement that we use to measure angles and temperature, and we use a special symbol to represent degrees ” ° “
example:
80°

Acute angle

An acute angle is always smaller than 90°.
acute angles are made between angles 0° – 90°

 

Right angle

A right angle is exactly 90°

We usually write angles with an arch-like below.

but for the right angle, instead of an arch, we put a square like below.

Obtuse angle

An obtuse angle is more than 90°­­­ but less than 180°.
example… in angle ∠XYZ  

Straight angle

A straight angle is exactly 180°. 

Reflex angle

 

A reflex angle is more than 180°. A reflex angle can be named in two ways.

example…
-90° = 270

 

Full rotation

A full rotation is when the angle is exactly 360° (back to 0°)

 

 

 

Protractor

A protractor is a type of ruler that is used to measure angles.

 

In the above picture, there is an arch equally divided into 180 equal parts. This arch is called a protractor.

Remember: each line is a degree. 

If you notice that there are numbers 0-180 clockwise and anticlockwise.
 that is is because if the base side of the angle is to the left then we need to measure form the numbers in the outer border and vice versa. If we do not follow this rule we will get the wrong measurement.

Example:

 you have an angle which the angle faces the left.

 

Now the angle would not make sense when we count the numbers in the inner border so count from the right. because…
we know that the angle above is obtuse. so if we start counting the angle from 180. We will know that the answer is 30° but 30 degrees is not an obtuse angle.

Measuring with a protractor

We are going to measure an angle using a protractor.
There are 3 cases while finding an angle with a protractor

 Case 1: Measure the angle XYZ

1. First, place the protractor on the angle. Make sure  the vertex of the angle is in the centre of the protractor
   
   
   
   
   
2. Then check if the base of the angle is facing the left or right.
   
   
   Our base of the angle is facing the right. so we need to count the numbers in the inner border
   
   
3. Now count from zero to where ever the second ray (Ray YX) is pointing
   
   
   
4. Now count the number starting from the baseline of the angle to the second Ray (  ray YX)
   
   in our example, we will get the answer 30.

Case 2: Find this angle 

1. First, we rotate the angle to either ray as the base.
   
2. Now count from zero to where ever the second ray (Ray YX) is pointing
3. Now count the number starting from the baseline of the angle to the second Ray (  ray YX)
   
   in our example, we will get the answer 30.

Case3: This is when there is a reflex angle and we need to find what angle it is.

Find ∠A

The angle we are going to find is reflex. and we need to find it with a  protractor. but a protractor can only measure 180°. so there is another way to measure reflex angles with a protractor

1. If you observe that the reflex part of the angle makes an obtuse angle…
   
   
   
2. so first we name the angle. in this example, we name it as ∠B. 
   
3. Then we measure the obtuse angle ∠B. ∠B is 140°
   
   
   
   
4. Remember that the full rotation of angle always  360°, 
   

   ∠A+∠B=360°

5. Then we have to minus the value of ∠B  from 360°. 

   ∠A+∠B=360°
   ∠B = 140°
   ∠A = 360°- ∠B
   ∠A = 360°- 140°
   ∠A =220°