According to Malus law, we have

$$I = {I_0}{\cos ^2}\theta \Rightarrow {I \over {{I_0}}} = {\cos ^2}\theta $$

Since the observed intensities are same for all values of $$\theta$$, therefore, for the angles given in options, the observed intensity should be same as well for all $$\theta$$, $$\theta$$ = 8$$^\circ$$, 38$$^\circ$$, 188$$^\circ$$ and 218$$^\circ$$, $${I \over {{I_0}}} \sim 0.9$$; and for $$\theta$$ = 203$$^\circ$$, $${I \over I} \sim 0.9$$.

Therefore, angle between direction of polarisation and x axis is 203$$^\circ$$.