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Find <EAD

Source: 1978 AHSME Problem 12

June 6, 2014
AMC

Problem Statement

In △ADE\triangle ADE, ∡ADE=140∘\measuredangle ADE=140^\circ, points BB and CC lie on sides ADAD and AEAE, respectively, and points A, B, C, D, EA,~B,~C,~D,~E are distinct.* If lengths AB, BC, CD,AB,~BC,~CD, and DEDE are all equal, then the measure of ∡EAD\measuredangle EAD is
<spanclass=′latex−bold′>(A)</span>5∘<spanclass=′latex−bold′>(B)</span>6∘<spanclass=′latex−bold′>(C)</span>7.5∘<spanclass=′latex−bold′>(D)</span>8∘<spanclass=′latex−bold′>(E)</span>10∘<span class='latex-bold'>(A) </span>5^\circ\qquad<span class='latex-bold'>(B) </span>6^\circ\qquad<span class='latex-bold'>(C) </span>7.5^\circ\qquad<span class='latex-bold'>(D) </span>8^\circ\qquad <span class='latex-bold'>(E) </span>10^\circ
* The specification that points A,B,C,D,EA,B,C,D,E be distinct was not included in the original statement of the problem. If B=DB=D, then C=EC=E and ∡EAD=20∘\measuredangle EAD=20^\circ.
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