document.write( "Question 945903: what is the sum of the exterior angles of a octogon \n" ); document.write( "
Algebra.Com's Answer #577003 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( " Solution:\r
\n" ); document.write( "\n" ); document.write( "1) Find the measure of \"one\" \"interior\" angle
\n" ); document.write( "2) From that, find the measure of one \"exterior\" angle
\n" ); document.write( "3) Multiply that by \"8\"
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\n" ); document.write( "\n" ); document.write( "1.\r
\n" ); document.write( "\n" ); document.write( "Find the measure of one interior angle\r
\n" ); document.write( "\n" ); document.write( "By memorization, the formula for the measure of an interior angle in a regular polygon of \"n\" sides is\r
\n" ); document.write( "\n" ); document.write( "\"%28+n+-2+%29%2A180+%2F+n\"\r
\n" ); document.write( "\n" ); document.write( "In an octagon, \"n+=+8\", so the formula is\r
\n" ); document.write( "\n" ); document.write( "\"%28+8+-2+%29%2A180+%2F+8\"\r
\n" ); document.write( "\n" ); document.write( "\"6%2A180+%2F+8\"\r
\n" ); document.write( "\n" ); document.write( "\"135\"º <-- the measure of each \"interior\" angle\r
\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "Find the measure of one \"exterior\" angle\r
\n" ); document.write( "\n" ); document.write( "Interior and exterior angles are \"supplements\", so the exterior angles are each
\n" ); document.write( "\"180+-+135+=+45\"º\r
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\n" ); document.write( "\n" ); document.write( "3.
\n" ); document.write( "Finding the sum of them all:\r
\n" ); document.write( "\n" ); document.write( "There are eight of these angles, so their sum is\r
\n" ); document.write( "\n" ); document.write( "\"8%2A45+=+360\"º\r
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\n" ); document.write( "\n" ); document.write( "Answer: \r
\n" ); document.write( "\n" ); document.write( "The sum of the measures of the \"exterior\" angles of a regular octagon is \"360\"º.
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