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P25 [Geometry] - Turkish NMO 1st Round - 2002

Source:

August 10, 2014
geometryrhombusfunctiontrigonometrytrig identitiesLaw of Cosines

Problem Statement

Let EE be a point on side [AD][AD] of rhombus ABCDABCD. Lines ABAB and CECE meet at FF, lines BEBE and DFDF meet at GG. If m(DAB^)=60∘m(\widehat{DAB}) = 60^\circ , what ism(DGB^)m(\widehat{DGB})?
<spanclass=′latex−bold′>a)</span> 45∘<spanclass=′latex−bold′>b)</span> 50∘<spanclass=′latex−bold′>c)</span> 60∘<spanclass=′latex−bold′>d)</span> 65∘<spanclass=′latex−bold′>e)</span> 75∘ <span class='latex-bold'>a)</span>\ 45^\circ \qquad<span class='latex-bold'>b)</span>\ 50^\circ \qquad<span class='latex-bold'>c)</span>\ 60^\circ \qquad<span class='latex-bold'>d)</span>\ 65^\circ \qquad<span class='latex-bold'>e)</span>\ 75^\circ
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