Can somone please help with this problem? Thank you so much in advance!!!

Answer: BPC = 105 degrees

Here is my graphical solution.  (I know it is not what you want.)

ABE is an equilateral triangle so all the angles are 60 degrees.

so

angle PBC= 30 degrees

so

angle BPQ=60 degrees

Now,

Angle QPC = angle DAC = 45 degrees     Corresponding angles on parallel lines

So  

That's easy.   

What's the measure of angle PAQ?