Problem
1972 AHSME Problem 21
![[asy] draw((3,-13)--(21.5,-5)--(19,-18)--(9,-18)--(10,-6)--(23,-14.5)--cycle); label("A",(3,-13),W);label("C",(21.5,-5),N);label("E",(19,-18),E);label("F",(9,-18),W);label("B",(10,-6),N);label("D",(23,-14.5),E); //Credit to Zimbalono for the diagram[/asy]](/static/aops/8824c3639f0d5ef50ae79cf637a0067af91fd8ae.png)
If the sum of the measures in degrees of angles A,~B,~C,~D,~E and F in the figure above is 90n, then n is equal to
\textbf{(A) }2\qquad \textbf{(B) }3\qquad \textbf{(C) }4\qquad \textbf{(D) }5\qquad \textbf{(E) }6
Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.
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