In a standard spur gear, is the pressure angle equal to the profile angle?

Simple answer, no. The pressure angle depends on the profile angle, or more accurately, the contact angle at the contact point.

If the gears are set right, they should touch on a tangent line that is tangent to both profiles. The pressure angle is perpendicular to this tangent.

Hope that helps.

There's multiple spur gear "standards", and all have different pressure angles.

Some geartooth shapes even have a variable pressure angle, as the gears rotate.

The profile angle? A new term for me....

However, the pressure angle is just that.. the angle of the pressure on the mating gear teeth.

Looking at your reference, they are not the same thing. The shape angle relates to the gear tooth form, and the pressure angle, as I stated above, is a different thing.

Go to Google and type spur gear design or calculator

They have some software to compute everything