document.write( "Question 233700: if the vertex of a regular polygon is 150 degrees what is the measure of the central angle \n" ); document.write( "

Algebra.Com's Answer #172512 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "All vertex angles (also called \"interior angles\") of a regular\r\n" );
document.write( "polygon have equal measures. If this regular polygon has n sides,\r\n" );
document.write( "then the sum of all the interior angles is 150° times n. The sum\r\n" );
document.write( "of the measures of all the interior angles of any polygon with n\r\n" );
document.write( "sides is (n-2) times 180°. So we have this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Solve that and we get \r\n" );
document.write( "\r\n" );
document.write( "So we have a 12-sided regular polygon (a regular dodecagon)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we'll connect all the vertices to the center,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are 12 central angles all\r\n" );
document.write( "with equal measure and since they\r\n" );
document.write( "all add up to 360°, each one is \r\n" );
document.write( "of 360° or 30°.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );