two regular polygons are such that the ratio between their number of sides is 1 is to 3 and the ratio of measure of the interior angles is 4 is to 7 find the number of sides of each polygon
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Two polygon in which the ratio between their number of sides is 1:2
Ratio of interior angles is 3:4
To find :
Side of each polygon
Solution:
The interior angle of the polygon is given by,
( (x-2) /x ) * 180
Let us take the sides as a and 2a.
substituting in the above formula, we get
((a-2)/a ) *180 / ((2a-2)/2a ) *180 = 3/4
(a-2)/a * 2/(a-1) = 3/4
(a-2) / (a-1) = 3/4
4a-8 = 3a-3
⇒ a=5
Therefore the sides are 5 and 10.
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