Points $P$ and $Q$ lie on the sides $AB$, $BC$ of the triangle $ABC$, such that $AC=CP =PQ=QB$ and $A \neq P$ and $C \neq Q$. If $\sphericalangle ACB = 104^{\circ}$, determine the measures of all angles of the triangle $ABC$.
Source: Polish Junior Math Olympiad 2020 First Round
Tags: geometry, easy
Points $P$ and $Q$ lie on the sides $AB$, $BC$ of the triangle $ABC$, such that $AC=CP =PQ=QB$ and $A \neq P$ and $C \neq Q$. If $\sphericalangle ACB = 104^{\circ}$, determine the measures of all angles of the triangle $ABC$.