In this post we will discuss the concept of angle and the different type of angle formation. In order to understand geometry it is very important to have clear concept of angles, that’s why we have made an effort to develop materials which is easy to understand.
Concept of Angles
What are angles?
An angle is formed when two rays are joined together at a common point. The angle is represented by the symbol ‘∠’.
Angles are generally measured in degrees.
How angle is formed?
Angle formation is very easy process.
Take two rays and join them at the common point after which you will get an angle.
Have a look at the following illustration
Parts of an angle
Node or Vertex – The common point is called node or vertex
Arms of the angle – The two rays are called arms of the angle.
Initial side is the reference side. All measurements are done using this side. The other side is terminal side.
Parts of Protractor
Protractor is a tool with the help of which you can easily find the angle between two line. The tool can be easily found at the local stationary shop and cheap price
How to measure an angle
To measure angle i.e., ∠AOB:
Step 1: Place the center point of the protractor on the vertex O.
Step 2: Adjust the base line of the protractor so that it is aligned with the line OB
Step 3: Read the value of angle AOB, from the inner scale.
Different Types of Angles
Angles are classified into different types, some of the notable distinctions is given below
2. Right angle
3. Obtuse angle
4. Straight angle
5. Reflex angle
6. Complete angle
Acute Angle – Angle whose measure is less than 90o is called acute angle
Right Angle – Angle whose measure is equal to 90o is called right angle
Obtuse Angle – Angle whose measure is greater than 90o but greater than 180o is called obtuse angle.
Straight Angle – Angle whose measure is equal to 180o is called straight angle.
Reflex Angle – Angle whose measure is greater than 180o but less than 360o is called reflex angle
Complete Angle – Angle whose measure is equal to 360o is called complete angle.
Important Properties of Angles
In this topic we will understand some important properties of angles which will be helpful to solve geometry questions in the future. Try to remember these points because they are important for your exams
If the sum of angles is equal to 90o then the angles are called complementary angles
∠AOC and ∠BOC are complementary angles
If the sum of angles is equal to 180o then the angles are called supplementary angles
∠AOC and ∠BOC are supplementary angles
Two angles with a common side and a common vertex are called adjacent angles
∠1 and ∠2 are adjacent angles
Vertically opposite angles
Angles that have a common vertex and whose sides are formed by the same line are called vertically opposite angles. Vertically opposite angles are equal in measure
(∠1 & ∠3) and (∠2 & ∠4) are vertically opposite angles
Alternate interior angles
Alternate interior angles are equal in measure. They are formed when two parallel lines are intersected by a transversal.
(∠1 & ∠3) and (∠2 & ∠4) are alternate interior angles
Alternate exterior angles
Alternate exterior angles are equal in measure. They are formed when two parallel lines are intersected by a transversal
(∠1 & ∠3) and (∠2 & ∠4) are alternate exterior angles
Angles which are in the same position in the figure when two parallel lines are intersected by transversal
Corresponding angles are equal in measure.
In the above figure, angle (2 & 3) are corresponding angles because they are in same position.
Similarly angle (1&4), (5&7) (8 & 6 ) are corresponding angles and are equal in measure
An Angle measured in Anti-Clockwise direction is Positive Angle
An angle measured in Clockwise direction is Negative Angle