The number of side of two regular polygons are in ratio 4:5 and the interior angle are in ratio 15:16 find the number of sides of each polygon

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  • 6
No of sides of the two polygons  is 4x, 5x  since ratio is 4:5

Interior angle of regular polygon of n sides is (n-2)180/n  = 180 - 360/n
thus for 4x sides it is 180 - 360/4x = 180 - 90/x
and for 5x sides it is 180- 360/5x = 180 - 72/x
ratio of the interior angles of 4x to 5x side is  15/16
so
(180 - 90/x)/(180 - 72/x) = 15/16
15(180 - 72/x)  = 16( 180 - 90/x)
15*180 - 15*72/x = 16*180 - 16*90/x
16*180 - 15*180 =  16*90/x - 15*72/x
180 = 360/x
x = 360/180 = 2
so no of sides are 8 and 10
  • 3
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