Question

please dont spam.

Need Quality Answers

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, number of sides of polygon be N.

Further given that, each exterior angle of a regular polygon < 40°.

We know,

Exterior angle of a regular polygon of n sides is given by

$\rm :\longmapsto\:\boxed{ \tt{ \: Exterior \: angle \: = \frac{360}{n} \: }}$

So,

$\rm :\longmapsto\:\dfrac{360}{N} < 40$

$\rm :\longmapsto\:\dfrac{9}{N} < 1$

$\rm :\longmapsto\:9 < N$

$\bf\implies \:N \: > \: 9 - - - (1)$

Also, Given that

Sum of interior angles of a polygon < 1980°

We know that,

Sum of interior angles of a polygon = (2n - 4)×90°

So,

$\rm :\longmapsto\:(2N - 4) \times 90 < 1980$

$\rm :\longmapsto\:(2N - 4) < 22$

$\rm :\longmapsto\:2N - 4 < 22$

$\rm :\longmapsto\:2N < 22 + 4$

$\rm :\longmapsto\:2N < 26$

$\bf\implies \:N \: < \: 13 \: - - - (2)$

So, From equation (1) and (2), we get

$\bf\implies \:9 < N < 13$

$\bf\implies \: N\: = \: 10, \: 11, \: 12$

Hence, N can assume 3 values

• Hence, Option (3) is correct.