For a particle on a sloped plane, the contact force from the plane has two components : the normal reaction and the friction force.
For a particle at rest on a slope, the friction force is equal to the component of the weight parallel to the slope but in the opposite direction. And the normal reaction is equal to the component of the weight perpendicular to the slope but in the opposite direction.
So overall the contact force must be equal to the weight but in the opposite direction. So the contact force is
mg and will have angle 90 - 60 = 30 degrees to the slope.