Definition
When two straight lines meet at a point they form an angle.
The point at which the arms meet (O) is known as the vertex of the angle.
The amount of turning from one arm (OA) to other (OB) is called the measure of the angle (ÐAOB) and written as m ÐAOB.
An angle is measured in degrees, minutes and seconds.
If a ray rotates about the starting initial position, in anticlockwise direction, comes back to its original position after 1 complete revolution then it has rotated through 360o.
1 complete rotation is divided into 360 equal parts. Each part is 1o.
Each part (1o) is divided into 60 equal parts, each part measures one minute, written as 1'.
1' is divided into 60 equal parts, each part measures 1 second, written as 1".Degrees -----> minutes --------> seconds
1o = 60'
In the figure, observe the different types of angles:
Right angle
An angle whose measure is 90o is called a right angle.
Acute angle
An angle whose measure is less then one right angle (i.e., less than 90o), is called an acute angle.
Obtuse angle
An angle whose measure is more than one right angle and less than two right angles (i.e., less than 180o and more than 90o) is called an obtuse angle.
Straight angle
An angle whose measure is 180o is called a straight angle.
Reflex angle
An angle whose measure is more than 180o and less than 360o is called a reflex angle.
Complete angle
An angle whose measure is 360o is called a complete angle.
Equal angles
Two angles are said to be equal, if they have the same measure.
Adjacent angles
Two angles having a common vertex and a common arm, such that the other arms of these angles are on opposite sides of the common arm, are called adjacent angles.
Complementary angles
If the sum of the two angles is one right angle (i.e., 90o), they are called complementary angles.
Supplementary angles
Two angles are said to be supplementary, if the sum of their measures is 180o.
Example:
Angles measuring 130o and 50o are supplementary angles.
Two supplementary angles are the supplement of each other.
Vertically opposite angles
When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles.
Angles Ð1 and Ð3 and angles Ð2 and Ð4 are vertically opposite angles.
Note:
Vertically opposite angles are always equal.Bisector of an angle
If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle.
Linear pair of angles
Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays.
Recall adjacent angles. Now observe the pairs of angles in the figure.
