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 #600577 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "If

is the number of sides and

, then the measure of each interior angle is an integer.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As

increases, the measure of the interior angles increases because

gets closer to 180 as

gets larger. A circle is the limiting shape as

increases without bound so a circle is an infinite-sided polygon with an infinite number of vertices with 180 degree interior angles. It was this idea that allowed Archimedes to approximate

by sandwiching a circle between two 96-sided polygons, one inscribed and the other circumscribed.\r
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\n" ); document.write( "\n" ); document.write( "As

increases, the measure of the exterior angles decreases because

gets smaller as

gets larger.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As

increases, the total of the measures of the interior angles increases because

gets larger as

gets larger.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As

increases, the total of the measures of the exterior angles remains constant because

does not change as

gets larger. Another way to put it is, no matter how many increasingly smaller turns you make, you still only go around one circle when you get back to where you started.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it\r
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