Problem

Source: Romania JBMO TST 2022

Tags: geometry, Romanian TST



Let $ABC$ be a triangle such that $\angle A=30^\circ$ and $\angle B=80^\circ$. Let $D$ and $E$ be points on sides $AC$ and $BC$ respectively so that $\angle ABD=\angle DBC$ and $DE\parallel AB$. Determine the measure of $\angle EAC$.