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Question

Determine the number of sides the polygon for which the ratio of the sum of the interior angles to the sum of the exterior angle is 5: 1.


Solution

Suppose number of sides be $$ n, $$ then
$$\dfrac{\text{sum of interior angles}}{\text{sum of exterior angles}}=\dfrac{5}{1}$$
$$ \Rightarrow \quad \dfrac{(2 n-4) \times 90^{\circ}}{360^{\circ}}=\dfrac{5}{1} $$
$$ \Rightarrow  2 n-4=20 $$
$$ \Rightarrow  n=12 $$

Mathematics

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