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Find the True Statement

Source: 1968 AHSME Problem #6

August 31, 2011
AMC

Problem Statement

Let side ADAD of convex quadrilateral ABCDABCD be extended through DD, and let side BCBC be extended through CC, to meet in point EE. Let SS represent the degree-sum of angles CDECDE and DCEDCE, and let S′S' represent the degree-sum of angles BADBAD and ABCABC. If r=S/S′r=S/S', then:
<spanclass=′latex−bold′>(A)</span> r=1 sometimes, r>1 sometimes<spanclass=′latex−bold′>(B)</span> r=1 sometimes, r<1 sometimes<spanclass=′latex−bold′>(C)</span> 0<r<1<spanclass=′latex−bold′>(D)</span> r>1<spanclass=′latex−bold′>(E)</span> r=1<span class='latex-bold'>(A)</span>\ r=1\text{ sometimes, }r>1\text{ sometimes} \qquad\\ <span class='latex-bold'>(B)</span>\ r=1\text{ sometimes, }r<1\text{ sometimes} \qquad\\ <span class='latex-bold'>(C)</span>\ 0<r<1\qquad <span class='latex-bold'>(D)</span>\ r>1 \qquad <span class='latex-bold'>(E)</span>\ r=1
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