Question

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio $1:5$.

Answer 1

We know that the sum of one exterior angle and one interior angle is $180°$ as they form a linear pair. Now lets say that the exterior angle is $x°.$ And it is given that the interior angle are in the ratio $1:5$

$\therefore$ the interior angle measure will be $5x$

Now,

$\Rightarrow x+5x=180°$

$6x=180°$

$x=30°$

Now, the sum of exterior angle in polygon $=360°$

Let the number of sides be ${}^{\prime }{n}^{\prime }$

$\therefore n.x=360°$

$n\times 30°=360°$

$n=12$

$\therefore$ The number of sides are $12$

Hence, the answer is $12.$