Find the number of sides in a regular polygon, if each interior angle is $144^{\circ}$

10

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11

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15

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Solution

The correct option is A $10$
Each interior angle of regular polygon of n sides is given by $\frac{180 (n - 2)}{n}$ degrees
$∴ \frac{180 (n - 2)}{n} = 144^{0}$
$\Rightarrow 180 (n - 2) = 144 n$
$\Rightarrow 180 n - 360 = 144 n$
$\Rightarrow 36 n = 360$
$\Rightarrow n = 10$

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Find the number of sides in a regular polygon, if each interior angle is 144∘

The correct option is A 10Each interior angle of regular polygon of n sides is given by 180(n−2)n degrees∴180(n−2)n=1440⇒180(n−2)=144n⇒180n−360=144n⇒36n=360⇒n=10

Find the number of sides in a regular polygon, if each interior angle is $144^{\circ}$

The correct option is A $10$
Each interior angle of regular polygon of n sides is given by $\frac{180 (n - 2)}{n}$ degrees
$∴ \frac{180 (n - 2)}{n} = 144^{0}$
$\Rightarrow 180 (n - 2) = 144 n$
$\Rightarrow 180 n - 360 = 144 n$
$\Rightarrow 36 n = 360$
$\Rightarrow n = 10$