Answer:
-19.09°.
Due to several approximations been applied in the detailed process, the angle given on image 2 (-18.17°) is slight minor compared to what can be obtained through direct calculations (-19.09°).
Check images below.
Note: If you want to calculate the length of the new vector, just need to apply the pythagorean theorem and taking the components of the result vector as if they were the 2 sides of a right triangle.
