I am not a power engineer, but I think the handwritten answer is the correct one. In the problem, the voltage is given as a COSINE function and the current as a SINE funtion. As you know, a cosine wave leads a sine wave by 90deg. Therefore, when you compare the angle phase shift between these V and I signals, you have to take into account also this -90 deg.
So the phase shift between the voltage and the current (using the voltage angle as reference) is:
ANG(current) - ANG(volt)=
(-30 deg) - (30 deg - 90 deg) = +30 deg
Therefore, the current leads the voltage by +30 deg