Question

Find the number of sides of that polygon whose exterior and interior angles are in the ratio 1 : 3.

Answer 1

Let no. of sides of polygon = $n$
Exterior angle $=x^{\circ }$
Interior angle $=3x^{\circ }$
$x^{\circ }+3x^{\circ }={180}^{\circ }$
($\because \text{sum of exterior angle and interior angle is}{180}^{\circ })$
$4x={180}^{\circ }⟹x={45}^{\circ }$
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Sum of all exterior angles $=(360{)}^{\circ }$
$\Rightarrow {45}^{\circ }\times n={360}^{\circ }$
Hence, n = 8.
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