Question

Find the radian measure of the interior angles of regular polygon of 18
sides..????​

Answer 1

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

We know that,

• In a regular polygon of 'n' sides,

$\: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf \: Exterior \: angle \: = \: \dfrac{360 \degree \: }{n}}$

and

$\: \: \: \: \: \: \: \: \: \boxed{ \sf \: Interior \: angle \: = \: 180\degree \: - Exterior \: angle}$

Now,

It is given that

• Number of sides of regular polygon, n = 18

$\rm :\implies\:Exterior \: angle = \dfrac{360\degree \:}{18}$

$\bf\implies \:Exterior \: angle = 20\degree \:$

So,

$\rm :\longmapsto\:Interior \: angle = 180\degree \: - Exterior \: angle$

$\rm :\longmapsto\:Interior \: angle = 180\degree \: - 20\degree \:$

$\rm :\longmapsto\:Interior \: angle = 160\degree$

$\rm :\longmapsto\:Interior \: angle = 160 \times \dfrac{\pi}{180}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \red{ \sf \: \because \: 1\degree \: = \dfrac{\pi}{180} \: radians}}$

$\bf\implies \:Interior \: angle \: = \dfrac{8\pi}{9} \: radians$

Additional Information :-

• 1. Sum of all interior angles of a polygon of n sided figure is (2n - 4) × 90°.

• 2. Sum of all exterior anglea of a polygon of n sided figure is 360°.

Answer 2

Answer:

π/9 radians

Step-by-step explanation:

Sum of all internal angles of a polygon is always equal to 2 π radians.

In a regular polygon all angles are identical.

So each internal angle= 2 π/18 = π/9 radians.