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Exterior angles of polygon - class-VII

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QuestionClick to flip

The interior angle of a regular polygon is double the exterior angle. Then the number in the polygon is

AnswerClick to flip back

$6$

💡 Explanation:

Let the number of sides in the polygon is $n$

Let the measure of exterior angles be $x$ respectively.

$\therefore$ Measure of interior angle $=2x$

So,

$\Rightarrow$ $n\times 2x=(2n-4)\times 90^o$

$\Rightarrow$ $nx=(n-2)\times 90^o$ ----- ( 1 )

Again we know that,

$\Rightarrow$ $nx=360^o$

$\Rightarrow$ $(n-2)\times 90^o=360^o$ [ From ( 1 ) ]

$\Rightarrow$ $n-2=4$

$\Rightarrow$ $n=6$

$\therefore$ The number of sides in the polygon are $6.$