Angles

Angles:


In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Greek (ankylοs), meaning "crooked, curved," and the English word "ankle." Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".

Let OA and OB two half lines with common end point O. The half lines OA and OB are the sides of an angle and the point O is the vertex of the angle. An angle is an amount of rotation of a half-line (or ray) in a plane about its end point from an initial position to a terminal position.We usually come across the questions such as how to measure an angle,what are the various methods to measure and angle etc,the explanation to these questions is given below.



Measurement of angle

The amount of rotation from initial side to terminal is called the measure of an angle.
Positive and Negative angles

Angles that are formed by counter clockwise (anti clockwise) rotation, such as the one shown in fig (ii) are said to be positive or to have positive measure.
Angles that are formed by a clockwise rotation, like the one in fig(iii) are said to be negative or to have negative measure.
Lines at right angles

The lines are said to be at right angles if the rotating half line (or ray) from starting from initial position to the final position describes one quarter of a circle.


Hope you like the above example of Angles.Please leave your comments, if you have any doubts.