document.write( "Question 1019530: the ratio of exterior angles and the interior angles of a regular polygon is 1:4. leena says the polygon is a regular decagon while linda says it is regular pentagon. who is right \n" ); document.write( "

Algebra.Com's Answer #635480 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "The ratio of exterior angles and the interior angles of a regular polygon is 1:4.
\n" ); document.write( "Leena says the polygon is a regular decagon while Linda says it is regular pentagon. who is right
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\n" ); document.write( "\n" ); document.write( "Answer. Leena is right.\r
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document.write( "Solution\r\n" );
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document.write( "Let x be the measure of the exterior angle, in degrees.\r\n" );
document.write( "Then the measure of the interior angle is  4x,  according to the condition.\r\n" );
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document.write( "And the sum of  x  and  4x  is  180 degrees:\r\n" );
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document.write( "x + 4x = 180  --->  5x = 180  --->  x =  = 36.\r\n" );
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document.write( "Thus the exterior angle is 36 degrees.\r\n" );
document.write( "(The interior is 4*36 = 144).\r\n" );
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document.write( "Now, the sum of exterior angles of any polygon is   degrees.\r\n" );
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document.write( "Hence, the number of vertices is   = 10.\r\n" );
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