AMC 12 2007a Problem 6

Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$. Point $D$ is inside triangle $ABC$, angle $ABC$ measures 40 degrees, and angle $ADC$ measures 140 degrees. What is the degree measure of angle $BAD$?

$\mathrm{(A)}\ 20 \mathrm{(B)}\ 30 \mathrm{(C)}\ 40 \mathrm{(D)}\ 50 \mathrm{(E)}\ 60$