MathDB

21

Part of 2009 National Olympiad First Round

Problems(1)

P inside ABC with 70, 10, 10, 40, x, 50 - x

Source: 0

4/28/2009
AB \equal{} AC, \angle BAC \equal{} 80^\circ. Let E E be a point inside △ABC \triangle ABC such that AE \equal{} EC and \angle EAC \equal{} 10^\circ. What is the measure of ∠EBC \angle EBC?
<spanclass=′latex−bold′>(A)</span> 10∘<spanclass=′latex−bold′>(B)</span> 15∘<spanclass=′latex−bold′>(C)</span> 20∘<spanclass=′latex−bold′>(D)</span> 25∘<spanclass=′latex−bold′>(E)</span> 30∘<span class='latex-bold'>(A)</span>\ 10^\circ \qquad<span class='latex-bold'>(B)</span>\ 15^\circ \qquad<span class='latex-bold'>(C)</span>\ 20^\circ \qquad<span class='latex-bold'>(D)</span>\ 25^\circ \qquad<span class='latex-bold'>(E)</span>\ 30^\circ