Magnitude of Sum of Two vectors Vector P and Vector q is given by

R^2 =p^2+q^2+2pqcos($)   __________________________(i)

Here $ indicates angle between them.

We are given 

R=p+q

So Squaring  both the sides we  get

R^2=p^2+q^2+2pq    ______________________(ii)

From (i) and (ii) we can write

P^2+q^2+2pqcos($)=p^2+q^2+2pq

Therefore 2pq=2pqcos($)

Cos($)=1

Therefore $=0

So angle between p vector and q vector is 0 degree.