Question

find the no of sides of regular polygon if each interior angle is 144​

Answer 1

Answer:

10 sides

Step-by-step explanation:

To find the no. of sides, we first need to find the measurement of the exterior angle.

Exterior angle =180∘ − measure of int. angle

= 180∘ − 144∘

= 36∘

To find the no. of sides, we use the formula

 ⇒360∘

measure of ext. angle

That is, no. of sides =

360∘

36∘

= 10 sides

Answer 2

Question:

If each interior angle of a regular polygon is 144° then find the number of sides of polygon..

Solution:

Formula:-

$\sf \looparrowright \large{\underline{\boxed{\dfrac{(n-2)180°}{n}}}}$$\green \star$

$\sf \implies{144°=\dfrac{(n-2)×180°}{n}}$

$\sf \implies{144°n=(n-2)180°}$

$\sf \implies{144°n=180°n-360°}$

$\sf \implies{144+360=180n}$

$\sf \implies{360=180n-144n}$

$\sf \implies{360=36n}$

$\sf \implies \dfrac{360}{36}=n$

$\sf \implies{\underline{\boxed{\color{blue}{n=10}}}}$$\red \star$

Hence the sides of polygon is 10