document.write( "Question 630504: Two lines bisect consecutive angles of a regular heptagon and and intersect in the heptagon's interior. Find the measure of the angle between the intersecting lines. \n" ); document.write( "
Algebra.Com's Answer #397052 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Given: OB bisects ∠ABC\r\n" );
document.write( "       OC bisects ∠BCD\r\n" );
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document.write( "To find: the measure of ∠BOC\r\n" );
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document.write( "[Note: if you had proved that OB and OC intersect at the center, you\r\n" );
document.write( "could just observe that ∠BOC is a central angle and has measure \"%22360%B0%22%2F7\".  \r\n" );
document.write( "But we will assume you haven't proved that.]  \r\n" );
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document.write( "The sum of the measures of the interior angles of an n-sided polygon\r\n" );
document.write( "is given by the formula (n-2)×180°\r\n" );
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document.write( "Since this is a heptagon, n=7 and the sum of the measures of the \r\n" );
document.write( "interior angles is (7-2)×180° = (5)×180° = 900°\r\n" );
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document.write( "Since this heptagon is regular, all the interior angles are congruent\r\n" );
document.write( "and have equal measure.  Therefore\r\n" );
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document.write( "m∠ABC = m∠BCD = \"%22900%B0%22%2F7\"\r\n" );
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document.write( "Since OB and OC bisect those interior angles,\r\n" );
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document.write( "m∠OBC = m∠OCB = \"1%2F2\"×\"%22900%B0%22%2F7\" = \"%22450%B0%22%2F7\"\r\n" );
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document.write( "Since the sum of the measures of the interior angles of ᐃBOC is 180°,\r\n" );
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document.write( "m∠OBC + m∠OCB + m∠BOC = 180°\r\n" );
document.write( "\"%22450%B0%22%2F7\" + \"%22450%B0%22%2F7\" + m∠BOC = 180°\r\n" );
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document.write( "                 \"%22900%B0%22%2F7\" + m∠BOC = 180°\r\n" );
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document.write( "                                  m∠BOC = 180° - \"%22900%B0%22%2F7\"\r\n" );
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document.write( "                                  m∠BOC = \"%221260%B0%22%2F7\" - \"%22900%B0%22%2F7\"\r\n" );
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document.write( "                                  m∠BOC = \"%22360%B0%22%2F7\" = \"51%263%2F7\"°\r\n" );
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document.write( "Edwin
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