Question

if each of exterior angle is twice its interior angle in a regular polygon find number of sides of the polygon

Answer 1

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Here's your answer...

Let the number of sides be n.
Then each exterior angle =
$\frac{360}{n}$
And each interior angle =
$\frac{(2n - 4) \times 90}{n}$
According to the question,
$\frac{360}{n} = 2 \times \frac{(2n - 4) \times 90}{n} \\ \frac{360}{n} = \frac{(2n - 4) \times 180}{n} \\ 360 = (2n - 4) \times 180 \\ 2n - 4 = \frac{360}{180} = 2 \\ 2n = 6 \\ n = 3$
The polygon has 3 sides.
Which means its a triangle.

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