Vx, Vy
...aaaactualy, it's quite simple:
climb at a constant airspeed, lets say the advertised Vx for your A/C at a given altitude, climb for 1,000' noting the elapsed time to gain the 1,000'
Now climb at a constant airspeed. lets say the advertised A/C's Vy speed for your A/C at a given altitude (and the same starting altitude you started at for Vx), climb for 1,000' noting the elapsed time.
You now have 4 numbers; the Vx IAS, the Vx time to gain 1,000', the Vy IAS and its time to gain 1,000'
correct the IAS to CAS then into TAS for the temp and pressure altitude for both Vx & Vy then convert the Kts or mph as the case may be into fpm.
Take the recorded times (in minutes) and divide them into the 1,000', yielding the climb rate for each of Vx & Vy
Noe take the ARCSIN (or use Mr. Pythogoras's Theorem if you prefer) of the climb rates divided by their respective TAS in fpm.
The resulting 2 angles will be the angle of climb for Vx and Vy.
You will find the Vx angle to be greater than the Vy angle.
The reason for that is there was a trade off between Vx's lower airspeed than Vy's shortening its horizontal (ground) distance traveled while not reducing it's climb rate proportionally.
This is of course performed in a homogeneous, stable inertial air mass and totally divorced from earth, short of gravity.
Some of the confusion over this is when attempting to clear an obstacle the pilot is totally focused on the obstacle and therefore in a subjective earth relative reference frame while the A/C remains in that air mass reference frame although close to an obstacle/ground the air mass is probably not an inertial one any more.
...aaaactually maybe this is not so simple.
What is confounding thou is none of the POHs give the climb rate at Vx, and none give the ground roll and total distance to clear a 50' obstacle at the Vy speed, probably because that data is not specified to be included in the GAMA Specification No.1 for POHs.
So angle of climb for Vx and Vy cannnot be obtained from POHs directly, it has to be derived.
When it is the Vy climb angle is always greater than the Vx climb angle.
There, I hope I've cleared all that up.