Answer
$1.57$
Work Step by Step
According to Snell's law,
$$n_{air}\sin\theta_1=n_{plastic}\sin\theta_2$$
where $n_{air}=1$, $\theta_1$ is the incident angle, and $\theta_2$ is the refraction angle.
$$ \sin\theta_1=n_{plastic}\sin\theta_2$$
According to the straight line formula $y=mx+b$ we can consider $\sin\theta_1=y$, $b=0$, $x=\sin\theta_2$, and $m={\rm slope}=n_{plastic}$.
So we need to plot dots of $\sin\theta_1$ and $\sin\theta_2$ and try to find the best-fit line then its slope will be the index of refraction of the plastic piece.
$$n_{plastic}={\rm slope}$$
From the graph below,
$$n_{plastic}=\color{red}{\bf 1.57}$$
