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Turkey NMO 2008 1st Round - P33 (Geometry)

Source:

August 27, 2012
geometryrhombusgeometric transformationreflectiontrapezoid

Problem Statement

Let EE be a point inside the rhombus ABCDABCD such that ∣AE∣=∣EB∣|AE|=|EB|, m(EAB^)=12∘m(\widehat{EAB})=12^\circ, and m(DAE^)=72∘m(\widehat{DAE})=72^\circ. What is m(CDE^)m(\widehat{CDE}) in degrees?
<spanclass=′latex−bold′>(A)</span> 64<spanclass=′latex−bold′>(B)</span> 66<spanclass=′latex−bold′>(C)</span> 68<spanclass=′latex−bold′>(D)</span> 70<spanclass=′latex−bold′>(E)</span> 72 <span class='latex-bold'>(A)</span>\ 64 \qquad<span class='latex-bold'>(B)</span>\ 66 \qquad<span class='latex-bold'>(C)</span>\ 68 \qquad<span class='latex-bold'>(D)</span>\ 70 \qquad<span class='latex-bold'>(E)</span>\ 72
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