Question

Q2. The measure of each interior angle of a regular polygon is 120°. Find the number of sides the polygon​

Answer 1

Answer:

180 ho sakta hai iska bhi

Answer 2

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

We know that

In a regular polygon,

$\boxed{ \bf{ \: interior \: angle + exterior \: angle = 180 \degree}}$

and

$\boxed{ \bf{ \: Number \: of \: sides \: (n) = \dfrac{360 \degree}{exterior \: angle} }}$

Understanding the statement :-

Since we have given the interior angle of a regular polygon and we have to find the number of sides. So firstly we find the exterior angle by using the formula and then we find number of sides.

Let's solve the problem now!!

Given that

• Interior angle of a regular polygon = 120°

So,

• Let Exterior angle of regular polygon is x°.

So,

• Using the formula,

$\rm :\longmapsto\:{ \sf{ \: interior \: angle + exterior \: angle = 180 \degree}}$

$\rm :\longmapsto\:120 \degree \: + x = 180\degree \:$

$\rm :\implies\:x = 60\degree \:$

Hence,

• Let number of sides of regular polygon be 'n'

So,

• Using Formula,

$\rm :\longmapsto\: \sf \: Number \: of \: sides \: (n) = \dfrac{360 \degree}{exterior \: angle}$

$\rm :\longmapsto\:Number \: of \: sides \: (n) = \dfrac{360 \degree}{x}$

$\rm :\longmapsto\:Number \: of \: sides \: (n) = \dfrac{360 \degree}{60\degree \:}$

$\rm :\longmapsto\:Number \: of \: sides \: (n) = 6$

Additional Information :-

1. Polygon :- A polygon having equal sides and equal angles is a regular polygon.

2. A regular polygon has three parts: 

• Sides 

• Vertices 

• Angles: interior and exterior 

3. Properties of regular polygon :-

• Sum of all exterior angles of a polygon = 360°

• Sum of all interior angles of polygon of 'n' sides = (2n - 4) × 90°.

• Three sided regular polygon is called equilateral triangle.