Question 23

The ratio between the sides of two regular polygons is 1 : 2. Ratio between their interior angles is 2 : 3. Find the number of sides of the polygons.

Solution

each interior angle = $$ \frac{(n - 2) 180^\circ}{n} $$

according to the question

$$ \frac{\frac{(n - 2) 180^\circ}{n}}{\frac{(2n - 2) 180^\circ}{2n}} = \frac{2}{3} $$

$$ \frac{(n - 2)180 \times 2n}{n (2n - 2)180} = \frac{2}{3} $$

$$ \frac{n - 2}{n - 1} = \frac{2}{3} $$

3n - 6 = 2n - 2

n = 4

sides are n = 4

$$ 2n = 2 \times 4 = 8 $$

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