We know that in standard position, the vertex of the angle should lie at the origin and its initial side is always fix along the positive x- axis. Please see the attached image.
We can see that the vertex of the angle is at the origin O and the initial side OB is along the positive x axis. This is the standard position of an angle.
Therefore, we have
An angle theta is in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis.