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Turkey NMO 2006 1st Round - P33 (Geometry)

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February 3, 2013
geometryangle bisector

Problem Statement

Let ABCDABCD be a convex quadrileteral such that m(ABD^)=40∘m(\widehat{ABD})=40^\circ, m(DBC^)=70∘m(\widehat{DBC})=70^\circ, m(BDA^)=80∘m(\widehat{BDA})=80^\circ, and m(BDC^)=50∘m(\widehat{BDC})=50^\circ. What is m(CAD^)m(\widehat{CAD})?
<spanclass=′latex−bold′>(A)</span> 25∘<spanclass=′latex−bold′>(B)</span> 30∘<spanclass=′latex−bold′>(C)</span> 35∘<spanclass=′latex−bold′>(D)</span> 38∘<spanclass=′latex−bold′>(E)</span> 40∘ <span class='latex-bold'>(A)</span>\ 25^\circ \qquad<span class='latex-bold'>(B)</span>\ 30^\circ \qquad<span class='latex-bold'>(C)</span>\ 35^\circ \qquad<span class='latex-bold'>(D)</span>\ 38^\circ \qquad<span class='latex-bold'>(E)</span>\ 40^\circ
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