Angles

Angles :When two rays meet at one point , the angle is formed. The common point is called the Vertex and the two rays are called the arms of the angle.



Here B is the vertex and AB and AC are two rays which are arms of the angle ABC.

Naming of Angle
There are several ways of naming of angles as discussed below :

1) While representing the name of angles the vertex should be in the middle and point on each arm on either side of the vertex.
Example :

The angle ABC is represented as ∠ABC or ∠CAB.

2) We name an angle by writing the letter at the vertex of the angle.
Example :

∠ABC is also denoted by ∠B.

3) The angle is also named by placing 1,2,3 etc. or small letter a,b,c etc. near the small circular arc connecting the two arms of the angle.

The angles are measured with the help of protractor. The measurements are in degrees. The degrees vary from 0 to 180. On the basis of the measurement there are different types of angles.

Interior and Exterior of an Angle

Consider ∠AOB. We observe that all points in the plane of ∠AOB can be divided into three groups :

i) Points which lie within the arms of the angle produced .

ii) Points which lie on the arms of the angle .

iii) Points which lie outside the arms of the angle.

Example :

Point P is in the interior of ∠AOB. Point Q is in the exterior of ∠AOB. Point A, B and O are on the ∠AOB.

Types of angle	Description
Acute angle	An angle lies between 00 and 900
Right angle	Whose measure is exactly 900
Obtuse angle	An angle whose measure is greater than 900 and less than 1800
Straight angle	Whose measure is exactly 1800
Reflex angle	An angle whose measure is greater than 1800

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Basic Geometry

• Point
• Lines
• Angles
• Lines - Angles
• Complementary-angles
• Supplementary-angles
• Vertically Opposite-Angles
• Linear Pair-Angles
• Adjacent- Angles
• Parallel Lines
• Solved Problems on Intersecting Lines
• Solved Problems on Parallel Lines
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