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P33 [Geometry] - Turkish NMO 1st Round - 2002

Source:

August 11, 2014
geometryrhombus

Problem Statement

Let ABCDABCD be a rhombus such that m(ABC^)=40∘m(\widehat{ABC}) = 40^\circ. Let EE be the midpoint of [BC][BC] and FF be the foot of the perpendicular from AA to DEDE. What is m(DFC^)m(\widehat{DFC})?
<spanclass=′latex−bold′>a)</span> 100∘<spanclass=′latex−bold′>b)</span> 110∘<spanclass=′latex−bold′>c)</span> 115∘<spanclass=′latex−bold′>d)</span> 120∘<spanclass=′latex−bold′>e)</span> 135∘ <span class='latex-bold'>a)</span>\ 100^\circ \qquad<span class='latex-bold'>b)</span>\ 110^\circ \qquad<span class='latex-bold'>c)</span>\ 115^\circ \qquad<span class='latex-bold'>d)</span>\ 120^\circ \qquad<span class='latex-bold'>e)</span>\ 135^\circ
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