Question

the ratio between the no. of sides of 2 regular polygons is 1:2 and ratio between the sum of their interior angles is 1:3. find the no. of sides

Answer 1

Hi friend!

Answer:

Number of sides of polygon A = x
Number of sides of polygon B = 2x

Sum of interior angles of polygon A = 180(x - 2)
= 180x - 360
Sum of interior angles of polygon B = 180(2x - 2)
= 360x - 360

Ratio between both = 1:3

$\frac{180x - 360}{360x - 360} = \frac{1}{3} \\ \\ 3(180x - 360) = 1(360x - 360) \\ 540x - 1080 = 360x - 360 \\ 540x - 1080 - 360x = - 360 \\ 540x - 360x = 1080 - 360 \\ 180x = 720 \\ x = 720 \div 180 = 4 \\ \\ x = 4$
So we got x as 4.

Number of sides of polygon A = x = 4
Number of sides of polygon B = 2x = 8

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