This problem was really challenging to me , I've spent much time on this but maybe it is easy to you guys . Enjoy !

Triangle $\displaystyle ABC$ has the following property : there is an interior point P such that $\displaystyle \angle PAB = 10^o $ , $\displaystyle \angle PBA = 20^o$ , $\displaystyle \angle PCA = 30^o$ and $\displaystyle \angle PAC = 40^o$ . Prove that triangle $\displaystyle ABC$ is isosceles .

Moderator edit:Approved Challenge question.