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Turkey NMO 2010 1st Round - P01 (Geometry)

Source:

July 26, 2012
geometry

Problem Statement

Let DD be a point inside of equilateral △ABC\triangle ABC, and EE be a point outside of equilateral △ABC\triangle ABC such that m(BAD^)=m(ABD^)=m(CAE^)=m(ACE^)=5∘m(\widehat{BAD})=m(\widehat{ABD})=m(\widehat{CAE})=m(\widehat{ACE})=5^\circ. What is m(EDC^)m(\widehat{EDC}) ?
<spanclass=′latex−bold′>(A)</span> 45∘<spanclass=′latex−bold′>(B)</span> 40∘<spanclass=′latex−bold′>(C)</span> 35∘<spanclass=′latex−bold′>(D)</span> 30∘<spanclass=′latex−bold′>(E)</span> 25∘ <span class='latex-bold'>(A)</span>\ 45^\circ \qquad<span class='latex-bold'>(B)</span>\ 40^\circ \qquad<span class='latex-bold'>(C)</span>\ 35^\circ \qquad<span class='latex-bold'>(D)</span>\ 30^\circ \qquad<span class='latex-bold'>(E)</span>\ 25^\circ
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