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Finding angle within rectangle

Source: AMC 10 2011 b Problem 18

February 24, 2011
geometryrectangletrigonometrytrig identitiesLaw of SinesAMCangles

Problem Statement

Rectangle ABCDABCD has AB=6AB=6 and BC=3BC=3. Point MM is chosen on side ABAB so that ∠AMD=∠CMD\angle AMD = \angle CMD. What is the degree measure of ∠AMD\angle AMD?
<spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 30<spanclass=′latex−bold′>(C)</span> 45<spanclass=′latex−bold′>(D)</span> 60<spanclass=′latex−bold′>(E)</span> 75 <span class='latex-bold'>(A)</span>\ 15 \qquad <span class='latex-bold'>(B)</span>\ 30 \qquad <span class='latex-bold'>(C)</span>\ 45 \qquad <span class='latex-bold'>(D)</span>\ 60 \qquad <span class='latex-bold'>(E)</span>\ 75
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