The ratio of the number of the sides of two regular polygon is 1:2,and the ratio of the sum of their interior angle is 3:8 Find the number of sides in each polygon?
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Answer:
Step-by-step explanation:
Since, the ratio of its internal to external angle is 7:2, you can say that
its internal angle = 7x and exterior angle = 2x.
Therefore,
7x + 2x = 180
=> x = 20
Exterior angle = 40 degrees
now (exterior angle) = 360/(no. of sides)
solving, you will get no. of sides = 9.
Answered by
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Answer:
Step-by-step explanation:
Let the no. of sides of the first polygon be x
Therefore, the no. of sides of the second polygon
Sum of interior angles is 180(n-2) where n is the number of sides
By problem ==>
180(x-2) / 180(2x-2) = 3/8
By cross - multiplying, we get ==>
8[180(x-2)] = 3[180(2x-2)]
1440x-2880 = 1080x-1080
1440x-1080x = -1080+2880
360x = 1800
x = 1800/360
Therefore, x = 5
2x = 2(5) = 10
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