MathNet 2015-part-02 — 191 problems (EN–VI) Question 73

Let $ABCD$ be a convex quadrilateral such that $\angle BAD = 50^\circ$, $\angle ADB = 80^\circ$ and $\angle ACB = 40^\circ$ holds. If $\angle DBC = 30^\circ + \angle BDC$, determine $\angle BDC$.