What's the appropriate range for the angle of a slide?
Per the Michigan State Handbook for Public
Playground Safety:

It is recommended that the average incline of a slide
chute be no more than 30 degrees. This can be measured
by determining that the height to length ratio (as shown
in Figure 18) does not exceed 0.577. No span on the
slide chute should have a slope greater than 50 degrees.

There is some other really good information in that booklet as well regarding the design of a slide.