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Question

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


Solution

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 $$'n'$$
$$\therefore n.x=360°$$
    $$n\times 30°=360°$$
    $$n=12$$
$$\therefore$$ The number of sides are $$12$$
Hence, the answer is $$12.$$


Mathematics

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