2016 AMC 12B Problem 4

The ratio of the measures of two acute angles is 5:4, and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the two angles?

\textbf{(A)}\ 75\qquad\textbf{(B)}\ 90\qquad\textbf{(C)}\ 135\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 270

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