If the ratio between the interior and exterior angles of a regular polygen is 8:1, then the polygen has - sides.

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Solution

The correct option is A
18

Let each interior angle $(i^{\circ}) = 8 x^{\circ}$ and
Each exterior angle $(e^{\circ}) = x$
We know ,
$i^{\circ} + e^{\circ} = 180^{\circ} 8 x + x = 180 9 x = 180 x = 20^{\circ} ∴ e^{\circ} = 20^{\circ} x = \frac{360^{\circ}}{e^{\circ}} = \frac{360^{\circ}}{20^{\circ}} = 18$

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If the ratio between the interior and exterior angles of a regular polygen is 8:1, then the polygen has - sides.

The correct option is A 18 Let each interior angle (i∘)=8x∘ and Each exterior angle (e∘)=x We know , i∘+e∘=180∘8x+x=1809x=180x=20∘∴e∘=20∘x=360∘e∘=360∘20∘=18