How to find how many degrees from the beginning to the end of the sunset? According to what I what told here there is 0.5 degrees from the beginning the end of the sunset. 

Unfortunately I didn't understand two things: 


  1) How can I prove in the simplest way that there's 0.5 degrees only
  from the beginning to the end of the sunset. 
  
  2) Why it is not adjust to my past observation on these phases (which
  was much longer (range from 5-7 minutes). which makes it between 1-2
  degrees.
The easiest way to measure the sun would be to use a pin-hole camera.

Use a piece of card with a pin hole. Hold it up so the sun shines through the pin hole and onto a piece of paper.  (Don't look at the sun through the hole - eye damage)

You will see a circle of light on the paper, this is the image of the sun. If the paper is 100cm from the card and the size of the image of the sun is $x$ cm, then you can work out the angular size of the sun.  It is about $\tan^{-1}(x/100)$ which is approximately $\frac{180x}{100\pi}$ You should get an angle of about 0.5 degrees.