Question

In a regular polygon the ratio of a interior angle to the number of sides is 20:1,What is the number of sides?

Answer 1

Answer:

the number of the side of a regular polygon is 10

Step-by-step explanation:

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Answer 2

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 ✅