Look at this picture of John Reynolds taking a curve.

Dont worry about air resistance or the motor's force, for now we only want to consider the motorcycle moving at a constant speed & radius through the curve.

Oops! I misspelled "provided".  Oh well.

What is the maximum speed the bike can take the curve?

Since F=ma, then F_c=ma_c.

Insert a_c= v²/r to get  F_c= mv²/r

Next, we account for static friction.  Why static and not kinetic?  Because the bike is not slipping along the radius; it maintains a constant radius.  If we were talking about the forward motion, we would use kinteic friction.  Anyway,

F_static= m_sN

If the bike went any faster, it would slide.  This means it is moving at the maximum speed possible, so we set friction = centriptal force to get...

m_sN = mv²/r

solve for v...              v = sqrt(rm_smg/m) =sqrt(rm_sg)

At what angle must he lean to maintain this path?

We want the angle marked "q".
To find it, look at the vectors...
We have the adjacent side: Fc
We have the opposite side: N
The angle, then = inv tan (N / Fc) = inv tan( g / (v²/r))