Angle between the stoppers

1615Ï€ ?

192 deg?

pressure on both the sides of the stopper has to be same for eqbm.

P₁=n₁RTV₁
P₂=n₂RTV₂

n₁V₁=n₂V₂ ...(1)

n₁=m/32 and n₂=m/28
if you consider volume of the tube to be V (just to keep it simple, because the terms (A,etc will cancel out)
then V₁=(2Ï€-α)V2Ï€
and V₂=αV2Ï€

now, the values just have to be put in (1)

because we are assuming the separator to be conducting(since nothing has been mentioned).
and if there is a temp. gradient, heat will flow from one to other, changing the temperature, which will subsequently cause a change in the pressure and volume.
hence, at equilibrium, temperature has to be the same.