document.write( "Question 979233: The following polygons are given. All of the polygons are
\n" ); document.write( "regular polygons.\r
\n" ); document.write( "\n" ); document.write( "Polygon a. Convex 15-gon
\n" ); document.write( "Polygon b. Convex 16-gon
\n" ); document.write( "Polygon c. Convex 17-gon
\n" ); document.write( "Polygon d. Convex 18-gon
\n" ); document.write( "Polygon e. Convex 19-gon
\n" ); document.write( "Polygon f. Convex 43-gon
\n" ); document.write( "Polygon g. Convex 44-gon
\n" ); document.write( "Polygon h. Convex 45-gon
\n" ); document.write( "Polygon i. Convex 46-gon
\n" ); document.write( "Polygon j. Convex 47-gon\r
\n" ); document.write( "\n" ); document.write( "1. Which polygon(s) has (have) interior angles that are whole
\n" ); document.write( "numbers (a number that is not a fraction or a decimal)? Explain
\n" ); document.write( "why it is that way.
\n" ); document.write( "2. What happens to the value of the interior angles as the
\n" ); document.write( "number of sides of the polygon increases? Explain your answer.
\n" ); document.write( "3. What happens to the value of the exterior angles as the
\n" ); document.write( "number of sides of the polygon increases? Explain your answer.
\n" ); document.write( "4. Explain what happens to the total sum of interior angles
\n" ); document.write( "as the number of sides in the polygon changes?
\n" ); document.write( "5. Explain what happens to the total sum of exterior angles
\n" ); document.write( "as the number of sides in the polygon changes? \n" ); document.write( "
Algebra.Com's Answer #600574 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The following polygons are given. All of the polygons are
\n" ); document.write( "regular polygons.\r
\n" ); document.write( "\n" ); document.write( "Polygon a. Convex 15-gon
\n" ); document.write( "Polygon b. Convex 16-gon
\n" ); document.write( "Polygon c. Convex 17-gon
\n" ); document.write( "Polygon d. Convex 18-gon
\n" ); document.write( "Polygon e. Convex 19-gon
\n" ); document.write( "Polygon f. Convex 43-gon
\n" ); document.write( "Polygon g. Convex 44-gon
\n" ); document.write( "Polygon h. Convex 45-gon
\n" ); document.write( "Polygon i. Convex 46-gon
\n" ); document.write( "Polygon j. Convex 47-gon\r
\n" ); document.write( "\n" ); document.write( "1. Which polygon(s) has (have) interior angles that are whole
\n" ); document.write( "numbers (a number that is not a fraction or a decimal)? Explain
\n" ); document.write( "why it is that way.
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document.write( "The sum of the interior angles of a polygon of n-sides is\r\n" );
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document.write( "\"%28n-2%29%2A%22180%B0%22\"\r\n" );
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document.write( "Since the polygons are regular, all the interior angles are the same,\r\n" );
document.write( "so each one is that expression divided by n\r\n" );
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document.write( "\"%28n-2%29%2A%22180%B0%22%2Fn\"\r\n" );
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document.write( "That must be equal to a whole number, say, W. Since n does not divide\r\n" );
document.write( "evenly into n-2, it must divide evenly into 180°. So we go through\r\n" );
document.write( "the list to see which numbers divide evenly into 180°:\r\n" );
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document.write( "Polygon a. Convex 15-gon, yes, since 15 divides evenly into 180°.\r\n" );
document.write( "Polygon b. Convex 16-gon, no\r\n" );
document.write( "Polygon c. Convex 17-gon, no\r\n" );
document.write( "Polygon d. Convex 18-gon, yes, since 18 divides evenly into 180°.\r\n" );
document.write( "Polygon e. Convex 19-gon, no\r\n" );
document.write( "Polygon f. Convex 43-gon, no\r\n" );
document.write( "Polygon g. Convex 44-gon, no\r\n" );
document.write( "Polygon h. Convex 45-gon, yes, since 45 divides evenly into 180°.\r\n" );
document.write( "Polygon i. Convex 46-gon, no\r\n" );
document.write( "Polygon j. Convex 47-gon, no\r\n" );
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\n" ); document.write( "2. What happens to the value of the interior angles as the
\n" ); document.write( "number of sides of the polygon increases? Explain your answer.
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\r\n" );
document.write( "\"%22%22=%22%22\"\"%22%22=%22%22\"\"%22180%B0%22%2A1\"\"%22%22=%22%22\"\"%22180%B0%22\"\r\n" );
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document.write( "So the value of the interior angles approaches 180° as the number \r\n" );
document.write( "of sides of the polygon increases.\r\n" );
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\n" ); document.write( "3. What happens to the value of the exterior angles as the
\n" ); document.write( "number of sides of the polygon increases? Explain your answer.
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\r\n" );
document.write( "The sum of the exterior angles of any polygon is 360°.  So\r\n" );
document.write( "each one of a regular polygon is \"%22%22=%22%22\"\"%220%B0%22\"\r\n" );
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document.write( "So the value of the exterior angles approaches 0° as the number \r\n" );
document.write( "of sides of the polygon increases.\r\n" );
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\n" ); document.write( "4. Explain what happens to the total sum of interior angles
\n" ); document.write( "as the number of sides in the polygon changes?
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\"%22%22=%22%22\"\"infinity\"\r\n" );
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\n" ); document.write( "5. Explain what happens to the total sum of exterior angles
\n" ); document.write( "as the number of sides in the polygon changes?
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\"matrix%282%2C2%2C%0D%0Alim%2C%28%22360%B0%22%29%2C%0D%0An-%22%22%3Einfinity%2C%22%22%29\"\"%22%22=%22%22\"\"%22360%B0%22\"\r\n" );
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document.write( "Edwin
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