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MathArt4

08.06.2017 04:50

In triangle ABC, $\angle$ A equals 120 degrees. A point D is inside the triangle such that $\angle$DBC = 2 $\times \angle $ABD and $\angle$DCB = 2 $\times \angle$ACD. Determine the measure, in degrees, of $\angle$ BDC. [asy][asy] pair A = (5,4); pair B = (0,0); pair C = (10,0); pair D = (5,2.5) ; draw(A--B); draw(B--C); draw(C--A); draw (B--D--C); label ("A", A, dir(45)); label ("B", B, dir(45)); label ("C", C, dir(45)); label ("D", D, dir(45)); [/asy][/asy]