Geometry
Angles
An angle is defined as the figure formed by the intersection of two lines or rays.
Parts of angles:
- Arms of an angle
- The two rays or the lines that meet at the common point to form an angle are called the arms of an angle.
- Vertex of an angle
- The point where the two arms meet is called the vertex of an angle.
In the figure, the ray OA and OB are the arms of an angle, and the point O is the vertex of an angle.
Naming angles
- The symbol that is used to name an angle is ∠.
- The three ways to name an angle are:
- Using only the vertex point.
- Using the vertex and a point of each arm.
- Using an alphabet or numbers.
Using only the vertex
- The vertex is at B.
- The angle is named ∠B.
- If two or more angles have the same vertex then the angle is not named by using only the vertex.
Using only the vertex and the points of each arm
- Three points are used to name the angle, one point on each arm and the vertex.
- While naming an angle the vertex is kept in the middle.
- The angle is named ∠CBA or ∠ABC.
Using the alphabets or the numbers
- The angle is named as ∠1 or ∠a.
- The lower-case English alphabet is used to name an angle.
- If two or more angles have the same vertex then the angle is named by either using the vertex and point of each arm or by numbers or letters.
The measure of an angle
- An angle is measured in degree.
- The symbol of the degree is “°”.
Protractor
- The instrument used to measure an angle is called a protractor.
- A protractor is semicircular in shape.
- It has degrees marked on it from 0° to 180° clockwise in the outer scale and anticlockwise in the inner scale.
Angles in our surrounding
The image below shows the angle in real-life objects.
Types of angles
Depending upon the measure of an angle, the angle is classified as
- Acute angle
- Right angle
- Obtuse angle
Acute Angle
Acute angle is defined as the angle which is more than 0° but less than 90°.
Examples:
Right Angle
The right angle is defined as the angle which is equal to 90°.
Examples:
Obtuse Angle
An obtuse angle is defined as the angle which is more than 90° but less than 180°.
Examples:
The figures below show all the three angles together.
Steps to measure angle using protractor
- Keep the protractor aligned to the base ray such that the base ray is at 0° or 180°.
- The number where the protractor coincides with the second ray gives the measure of the angle.
Examples:
Measure the angle shown in the protractor.
Solution:
The image shows that one ray is at 0° and the other ray is at 110°.
Therefore, the angle shown on the protractor is 110°.
Fun facts:
Did you know?