LINES AND ANGLES
Angle: An angle is the union of two different rays having the same initial point (or) Amount of rotation. The common point is called the vertex. The size of an angle is typically measured in degrees
Representing an angle:
Generally we use three capital letters to represent an angle. The above angle is represented by \(\angle AOB\)\(\angle {AOB}\) (or) \(\angle {BOA}\) \(\angle BOA\) and is read as ‘angle AOB’ or ‘angle BOA’. Note that the middle letter denotes the vertex of the angle. The symbol \(\angle\) stands for angle. It can also be represented by \(\angle O\). Some times we use numbers or lower case letter to denote angles.
Consider the following angles:
Interior and exterior of an angle:
An angle divides the plane into three regions.
i) Point belongs to the angle:
If any point (like P) lying on one of its arms, then that ‘P’ belongs to the angle
ii) Interior of an angle: In the following figure, ‘S’ does not belong to the angle. Note that the points ‘S’ and ‘P’ are on the same side of the \(\mathop {OB}\limits^{\xrightarrow{{}}} \) and the points ‘S’ and ‘P’ are also on the same side of the \(\mathop {OA}\limits^{\xrightarrow{{}}} \). Such a point is said to be in the interior of the angle.
iii) Exterior of an angle: In the following figure, ‘G’ does not belong to the angle. It is not in the interior of the angle. We say that it is in the exterior of the angle.
Magnitude of an angle: The magnitude of an angle is the amount of rotation through which one of the arms must be rotated about the vertex to bring it to the position of the other.
Measure of an angle: To find out the magnitude to a given angle, we need a standard unit angle. Then we can compare the given angle with the unit angle and say its measure.
i) A quarter turn of a ray \(\mathop {OA}\limits^{\xrightarrow{{}}} \) about O describes an angle which is called a right angle.
ii) Units for measuring angle:
A right angle is divided into 90 equal parts and each part is called a degree. Degree is the unit for measuring an angle.
One degree is written as 1°. One degree is divided into 60 equal parts and each part is called a minute. One minute is divided into 60 equal parts and each part is called a second. 1 minute is denoted by 11 . 1 second is denoted by 111.
10 = 601 (read as 60 minutes)
11 = 6011 (read as 60 seconds).