how to find the DC motor turning angle using encoder?
how to fix the DC motor to turn at specific angle using this
  information?


You develop a small control system. From the "neutral" position the demand to move can be translated into a demand to increment "so-many" pulses. So, you turn on the motor and count the pulses (digitally) and when the required pulse count is met, you turn off the motor. However, there may be overshoot so you will need to reverse your motor direction (possibly using a H bridge) to bring it back to the target position demanded.

This then becomes a problem that may be solved with a 3 term (PID) controller should the position continue to oscillate and there are many algorithms to solve this with usually the simplest being that as you approach the target count you slow down the speed of the motor.