1958 AHSME Problem 29

In a general triangle ADE (as shown) lines \overline{EB} and \overline{EC} are drawn. Which of the following angle relations is true?

\begin{array}{l} \textbf{(A)}\ x + z = a + b\qquad \textbf{(B)}\ y + z = a + b\qquad \textbf{(C)}\ m + x = w + n\qquad \\ \textbf{(D)}\ x + z + n = w + c + m\qquad \textbf{(E)}\ x + y + n = a + b + m \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.