The equation of a curve is \(xy = 12\) and the equation of a line \(l\) is \(2x + y = k\), where \(k\) is a constant.

In the case where \(k = 10\), one of the points of intersection is \(P(2, 6)\). Find the angle, in degrees correct to 1 decimal place, between \(l\) and the tangent to the curve at \(P\).