West, and Somewhere North

A weather balloon is tracked from its launch pad. The tracking station never stores the balloon's two coordinates directly — it stores the length of the displacement and only the east–west part of it:

Set up a plane where the positive $x$-axis points east and the positive $y$-axis points north, and let the displacement be the vector

$\vec{d} = (d_x,\ d_y)$

In what direction does $\vec{d}$ point, measured as an angle turned counterclockwise from due east?

Give the angle in degrees in the range $0^\circ \le \theta < 360^\circ$, rounded to two decimal places.