How many pairs of regular Polygons are possible whose interior angles are in ratio 10 : 9 ?
Answers
Given : interior angles of regular polygon are in ratio 10 : 9
To find : How many pairs of regular Polygons are possible
Solution:
Interior angle of a regular polygon
= (n - 2)* 180 /n n > 2
Let say number of Sides are A & B of polygon whose interior angles are in ratio 10 : 9
A , B > 2
=> (A - 2)* 180/A : (B - 2)* 180/B :: 10 : 9
=> ( (A - 2)* 180/A)/ ((B - 2)* 180/B) = 10/9
=> 9 (A - 2) B = 10(B - 2) A
=> 9AB - 18B = 10AB - 20A
=> -18B = AB - 20A
=> -18B = A(B - 20)
=> A = 18B/(20-B)
=> 2 < B < 20
Checking all B for which A is integer
B A
5 6
8 12
10 18
11 22
12 27
14 42
15 54
16 72
17 102
18 162
19 342
11 possible Pairs
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Step-by-step explanation:
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