Question

The ratio between the number of sides of
two regular polygons is 3 : 4 and the ratio
between the sum of their interior angles is
2 : 3. Find the number of sides in each
polygon.
​

Answer 1

Answer:

CORRECT ANSWER IS

6 and 8  / 8 and 6

Step-by-step explanation:

Sum of  interior angles  regular polygons = (n−2)∗180

sides of two regular polygons= x and y

So, x/y=3/4

x=3y/4

Sum of  interior angles  regular polygons (x)=(x−2)∗180

Sum of  interior angles  regular polygons (y)=(y−2)∗180

(x−2)∗180/(y−2)∗180=2/3

x−2/y−2=2/3

3y/4−2/y−2=2/3

3y−8/y−2=8/3

9y−24=8y−16

y=8

x=3y/4=3∗8/4=6

Answer (A) 6 and 8, (D) 8 and 6.

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