Is it possible to explain the difference between synodic month and sidereal month by degrees? Is it possible to explain the difference between synodic and sidereal month by degrees - in the following way? 

Just recently I learnt about these two types of months, and I want to see if I can understand the difference by degrees method. Assuming the orbit's moon is 360 degrees, the sidereal month starts from the point where 1st degree to (include) 1st degree, while the synodic month starts from 1st degree to the 0.5 degree (after full orbit's moon, because the angular size of the moon is 0.5 degree). Is it possible to understand why it that's way?
A better diagram is something like this:

 


Day 0. The Moon is aligned with the Sun (New Moon) and some star X behind the Sun (of course :-), as shown by the arrow at 1. (Neither the Sun nor the star X are shown in the figure.)
Day 27.32. One sidereal month after figure 1. The Moon has travelled through 360 degrees orbiting around the Earth. (During that time, an arrow from the Earth through the Moon is pointing at different stars.) After one sidereal month, the Moon is again aligned with star X, as shown by the solid arrow in figure 2. (The arrow in 1 and 2 are parallel because the star is very far away.) Because the Earth has moved in its orbit around the Sun, the position of the Sun (shown by the dashed arrow in figure 2) has changed relative to figure 1. The Moon is still a few days prior to New Moon. 
Day 29.53. One synodic month after figure 1. The Moon is again aligned with the Sun (New Moon), as shown by the solid arrow in figure 3. The direction to star X is shown by the dashed arrow which is parallel to the solid arrows in figures 1 and 2.


Note how the arrows pointing to the Sun all point to the center of the Earth's orbit while the arrows pointing to star X are parallel.

You are probably interested in the angle between the two arrows in position 3; that is, how far has the Moon moved in its orbit from the position of the sidereal month to the position of the synodic month. The average angle = (360 degrees)/(27.32 days) * (29.53-27.32 days) = 29.12 degrees.