LINES AND ANGLES

 LINES AND ANGLES
Operations with angles:

Consider \(\angle{AOB}\)  and \(\angle{BOC}\) in the above figure. Both  \(\angle{AOB}\)  and \(\angle{BOC}\) have a common arm \(\mathop {OB}\limits^{\xrightarrow{{}}} \) and a common vertex ‘O’.     . 
\(\therefore \,\,\,\angle AOC = \angle AOB + \angle BOC\)
Bisector of the angle:
    i)  
         
  \(\angle PQS\,\,\,and\,\,\,\angle SQR\) have the same measure and congruent. So \(\overrightarrow {QS} \) is called the bisector of  \(\angle PQR\). A ray which divides an angle into two congruent angles is called the bisector of the angle.
    ii)
                                                                
 In the above figure, \(\angle AOE\) is divided into four congruent angles.