Since the x-coordinate of the point is negative and the y-coordinate is positive, the point is in the second quadrant (90° < angle < 180°)
Then, in order to find the angle, we can use the relations:
[tex]\begin{gathered} \cos (\theta)=-\frac{\sqrt[]{2}}{5} \\ \sin (\theta)=\frac{\sqrt[]{23}}{5} \end{gathered}[/tex]
Using a calculator and knowing that the angle is between 90° and 180°, we have:
[tex]\begin{gathered} \theta=\cos ^{-1}(-\frac{\sqrt[]{2}}{5})=106.4\degree \\ \theta=\sin ^{-1}(\frac{\sqrt[]{23}}{5})=106.4\degree \end{gathered}[/tex]
So the angle is 106.4°.
