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Turkey NMO 2008 1st Round - P01 (Geometry)

Source:

August 23, 2012
geometrycircumcircle

Problem Statement

Let ADAD be a median of △ABC\triangle ABC such that m(ADB^)=45∘m(\widehat{ADB})=45^{\circ} and m(ACB^)=30∘m(\widehat{ACB})=30^{\circ}. What is the measure of ABC^\widehat{ABC} in degrees?
<spanclass=′latex−bold′>(A)</span> 75<spanclass=′latex−bold′>(B)</span> 90<spanclass=′latex−bold′>(C)</span> 105<spanclass=′latex−bold′>(D)</span> 120<spanclass=′latex−bold′>(E)</span> 135 <span class='latex-bold'>(A)</span>\ 75 \qquad<span class='latex-bold'>(B)</span>\ 90 \qquad<span class='latex-bold'>(C)</span>\ 105 \qquad<span class='latex-bold'>(D)</span>\ 120 \qquad<span class='latex-bold'>(E)</span>\ 135
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