Question

find the number of sides of regular polygon whose each exterior angle has a measure of 45 (by step by step )​

Answer 1

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

Exterior angle of a regular polygon = 45°

$\large\underline{\sf{To\:Find - }}$

Number of sides of regular polygon.

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

Given that

• Exterior angle of a regular polygon = 45°

Let assume that

• Number of sides of regular polygon be n.

We know that,

$\rm :\longmapsto\:number \: of \: sides = \dfrac{360 \degree}{Exterior \: angle}$

$\rm :\longmapsto\:n \: = \: \dfrac{360}{45}$

$\bf\implies \:n = 8$

Hence,

• Number of sides of regular polygon = 8

Additional Information :-

In regular polygon, of n sides,

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

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

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

$\boxed{ \sf{ \: n = \dfrac{360}{180 - Interior \: angle} }}$

$\boxed{ \sf{ \: Sum \: of \: all \: Interior \: angles = (n - 2) \times 180}}$

$\boxed{ \sf{ \: Sum \: of \: all \: Exterior \: angles = 360}}$

Answer 2

Step-by-step explanation:

Question:- Find the number of sides of regular polygon whose each exterior angle has a measure of 45°

Solution:- Let the number of sides be n

Sum of all exterior angle of n side regular polygon = 360°

∴ each exterior angle = 360°/n

According to question 45° = 360°/n

➥ 45° n = 360°

➥ n = 360°/45° = 8

➥ n = 8

Number of sides = 8 Ans.

:)