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1993 AMC 12 #2 - Triangle

Source:

January 2, 2012
AMC

Problem Statement

In △ABC\triangle ABC, ∠A=55∘\angle A=55^{\circ}, ∠C=75∘\angle C=75^{\circ}, DD is on side AB‾\overline{AB} and EE is on side BC‾\overline{BC}. If DB=BEDB=BE, then ∠BED=\angle BED= [asy] size((100)); draw((0,0)--(10,0)--(8,10)--cycle); draw((4,5)--(9.2,4)); dot((0,0)); dot((10,0)); dot((8,10)); dot((4,5)); dot((9.2,4)); label("A", (0,0), SW); label("B", (8,10), N); label("C", (10,0), SE); label("D", (4,5), NW); label("E", (9.2,4), E); label("55∘55^{\circ}", (.5,0), NE); label("75∘75^{\circ}", (9.8,0), NW); [/asy] <spanclass=′latex−bold′>(A)</span> 50∘<spanclass=′latex−bold′>(B)</span> 55∘<spanclass=′latex−bold′>(C)</span> 60∘<spanclass=′latex−bold′>(D)</span> 65∘<spanclass=′latex−bold′>(E)</span> 70∘ <span class='latex-bold'>(A)</span>\ 50^{\circ} \qquad<span class='latex-bold'>(B)</span>\ 55^{\circ} \qquad<span class='latex-bold'>(C)</span>\ 60^{\circ} \qquad<span class='latex-bold'>(D)</span>\ 65^{\circ} \qquad<span class='latex-bold'>(E)</span>\ 70^{\circ}
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