document.write( "Question 205368This question is from textbook Longman Mathematics for IGCSE Book 1
\n" ); document.write( ": There are two polygons. The larger one has three times as many sides as the smaller one, and its angle sum is four times bigger. How many sides has the smaller polygon? \n" ); document.write( "
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There are two polygons. The larger one has three times as many sides as the smaller one, and its angle sum is four times bigger. How many sides has the smaller polygon?
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\n" ); document.write( "If a polygon has x sides, then each angle of this polygon is:
\n" ); document.write( "180 - (360/x)
\n" ); document.write( "the angle sum of this polygon
\n" ); document.write( "= x * (180 - (360/x))
\n" ); document.write( "= 180x - 360 \r
\n" ); document.write( "\n" ); document.write( "let:
\n" ); document.write( "number of smaller polygon's side = a
\n" ); document.write( "angle sum of smaller polygon = 180a - 360
\n" ); document.write( "number of larger polygon's side = b
\n" ); document.write( "angle sum of larger polygon = 180b - 360 \r
\n" ); document.write( "\n" ); document.write( "b = 3a
\n" ); document.write( "180b - 360 = 5 * (180a - 360)
\n" ); document.write( "4 times bigger is 5 times as big.
\n" ); document.write( "4 times bigger is 5 times as big.
\n" ); document.write( "4 times bigger is 5 times as big.
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\n" ); document.write( "How much is 1 times bigger, or 100% bigger? It's 2 times as big.
\n" ); document.write( "180*(3a) - 360 = 900a - 1800
\n" ); document.write( "540a - 360 = 900a - 1800
\n" ); document.write( "a = 4
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