737 LNAV INTERCEPT ANGLE
 

Does anyone know LNAV intercept angle?
when I engage LNAV, airplane try to intercept 90 degree angle , even if it was already turn to final course.

It should be in your FCOM relating to the software version you have; but it used to be 45 degrees. If you were in a turn to an ATC intercept HDG and selected LNAV it would turn onto a 45 degree intercept. This was with software >2 years ago.
Thus you only selected LNAV when wings were level.
Likewise; if you selected a 'route offset' and selected LNAV it would turn onto a 45 degree intercept.

LNAV engages when laterally within 3 nautical miles of the active route leg. If outside of 3 nautical miles of the active route leg, LNAV engages if on an intercept heading of 90 degrees or less and the intercept will occur before the active waypoint.

Remember that when you press LNAV during a turn, it will use the track when pressed to intercept, thus will roll out of the turn to establish in the track you passed when pressing LNAV instead of completing the turn... Ensure when pressing LNAV you are wings level to avoid the roll back onto track before intercept.

THE 1% RULE.
Try this it works.Employ the 1% rule.At 1% of your current ground speed, distance from your LNAV track (cross track error or distance from) select a heading towards your next LNAV track and then press the LNAV button.Works regardless of speed.For example if you try to use LNAV to join a DME arc at too high a speed 320 knots etc, it often will overshoot the arc, but if you commence your turn at 1% GS in NM you will roll out on the arc.....Peter

Combine what Rat and Sky stated.

In regards to 45/90, I have seen both depending on the brand, variant, and FMS.