Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 8"

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8. Let <math>ABCDE</math> be a convex pentagon with <math>AB\sqrt{2}=BC=CD=DE</math>, <math>\angle ABC=150^\circ</math>, <math>\angle BCD=75^\circ</math>, and <math>\angle CDE=165^\circ</math>. If <math>\angle ABE=\frac{m}{n}^\circ</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m+n</math>.
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==Problem==
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Let <math>ABCDE</math> be a convex pentagon with <math>AB\sqrt{2}=BC=CD=DE</math>, <math>\angle ABC=150^\circ</math>, <math>\angle BCD=75^\circ</math>, and <math>\angle CDE=165^\circ</math>. If <math>\angle ABE=\frac{m}{n}^\circ</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m+n</math>.
  
[[Mock AIME 1 2006-2007]]
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==Solution==
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{{solution}}
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----
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*[[Mock AIME 1 2006-2007/Problem 7 | Previous Problem]]
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*[[Mock AIME 1 2006-2007/Problem 9 | Next Problem]]
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*[[Mock AIME 1 2006-2007]]

Revision as of 19:39, 22 August 2006

Problem

Let $ABCDE$ be a convex pentagon with $AB\sqrt{2}=BC=CD=DE$, $\angle ABC=150^\circ$, $\angle BCD=75^\circ$, and $\angle CDE=165^\circ$. If $\angle ABE=\frac{m}{n}^\circ$ where $m$ and $n$ are relatively prime positive integers, find $m+n$.

Solution

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