The angle between the vectors is 80.6 degrees
How to find the angle
The angle (say x) between two vectors can be found using the dot product formula
The dot product of vectors:
v . w = (-12) * (4) + (5)(17)
v . w = 37
The magnitudes of the vectors
v = √{(-12)² + (5)²} = √{144 + 25} = √169 = 13
w = √{(4)² + (17)²} = √{16 + 289} = √305
Solving for the angle, s
cos x = 37 / (13 * √305)
x = arcos { 37 / (13 * √305) }
x = 80.621
x = 80.6 degrees (to the nearest tenth of a degree)