Interior angle of a 'n ' sided convex polygon are in G.P .. smallest angle is 1^o and

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8. Sequences and Series

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The interior angle of a $'n$' sided convex polygon are in $G.P$.. The smallest angle is $1^o $ and common ratio is $2^o $ then number of possible values of $'n'$ is

A

$0$

B

$1$

C

$2$

D

none of these

Solution

$1\left[2^{n}-1\right]=(n-2) \cdot 180$

$359+2^{n}=180 n$

$L.H.S.$ odd number

$R.H.S$ even number

no $'n'$ possible.

Standard 11

Mathematics

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