In a regular polygon the ratio of a interior angle to the number of sides is 20:1,What is the number of sides?
In a regular polygon the ratio of a interior angle to the number of sides is 20:1,What is the number of sides?
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Answer:
the number of the side of a regular polygon is 10
Step-by-step explanation:
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Answer:
Number of sides =3 or 6
Step-by-step explanation:
Given:-
In a regular polygon the ratio of a interior angle to the number of sides is 20:1
To find:-
What is the number of sides?
Solution:-
We know that,
The Interior angle of a regular polygon of "n" sides=[(n-2)/n]×180°
The ratio of an interior angle to the number of sides=20:1
=>[(n-2)/n]×180°:n=20:1
=>[(n-2)/n]×180°/n=20/1
=>[(n-2)/n²]×180°=20
=>(n-2)/n²=20/180
=>(n-2)/n²=1/9
On applying cross multiplication then
=>n²×1=9(n-2)
=>n²=9n-18
=>n²-9n+18=0
=>n²-6n-3n+18=0
=>n(n-6)-3(n-6)=0
=>(n-6)(n-3)=0
=>n-6=0 or n-3=0
=>n=6 or n=3
Answer:-
Number of sides in the regular polygon=3 or 6
Check:-
1)If n=3 then the interior angle
=[(3-2)/3]×180°
=>180°/3=60°
Ratio of interior angle to number of sides
=60°:3=20:1
2)If n=6 then the interior angle
=[(6-2)/6]×180°
=>4×180°/6
=>4×30°
=>120°
Ratio of interior angle to number of sides
=120°:6
=20:1
Verified ✅