Math, asked by Sakshi2511, 1 year ago

Each interior angle of a regular polygon is double of its exterior angle .Find the number of sides in the polygon.( WITH PROPER STATEMENTS PLEASE)

Answers

Answered by Bunti360
32
Let exterior angle be x,
Now each interior angle is 2x, From the data,

We know that interior angle + Exterior angle is always 360°,

Now x + 2x = 360°
=> 3x = 360°,
=> x = 120°, So each interior angle is 120°,

We know that interior angle of a regular polygon is,

 \frac{(n - 2) \times 180}{n}

Now using that fromula, We need to find n,

=> 180n - 360 = 120n, Since each interior angle is 120°
=> 60n = 360°,

=> n = 6,

Therefore the Polygon is Hexagon which is 6 sided polygon,

Hope you understand, Have a great day !!

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Answered by Abhay111111111
13
Let Be x
Now x + 2x = 360° 
=3x = 360°,
=x = 120°,
So each interior angle is 120°,
180n - 360 = 120n ex a 120°
=60n = 360°

=n = 6
this is right
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