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Turkish NMO First Round - 2012 Problem - 17 {Geometry}

Source:

July 1, 2012
geometrytrigonometrygeometric transformationreflectionsymmetryangle bisector

Problem Statement

Let DD be a point inside △ABC\triangle ABC such that m(BAD^)=20∘m(\widehat{BAD})=20^{\circ}, m(DAC^)=80∘m(\widehat{DAC})=80^{\circ}, m(ACD^)=20∘m(\widehat{ACD})=20^{\circ}, and m(DCB^)=20∘m(\widehat{DCB})=20^{\circ}. m(ABD^)=?m(\widehat{ABD})= ?
<spanclass=′latex−bold′>(A)</span> 5∘<spanclass=′latex−bold′>(B)</span> 10∘<spanclass=′latex−bold′>(C)</span> 15∘<spanclass=′latex−bold′>(D)</span> 20∘<spanclass=′latex−bold′>(E)</span> 25∘ <span class='latex-bold'>(A)</span>\ 5^{\circ} \qquad <span class='latex-bold'>(B)</span>\ 10^{\circ} \qquad <span class='latex-bold'>(C)</span>\ 15^{\circ} \qquad <span class='latex-bold'>(D)</span>\ 20^{\circ} \qquad <span class='latex-bold'>(E)</span>\ 25^{\circ}
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