Question

the ratio between the interior and exterior angle of a regular polygon is 3:2, find the the number of sides of a polygon​

Answer 1

$\huge\rm\underline\pink{GIVEN:}$

• $\large\rm{Ratio\:of\:interior\:and\:exterior\:angle\:of\:Regular\:polygon\:=\:3:2}$

$\huge\rm\underline\pink{TO\:FIND:}$

• $\large\rm{Number\:of\:sides\:of\:polygon}$

$\huge\rm\underline\pink{SOLUTION:}$

$\large\rm{Let\:the\:Interior\:angle\:be\:3x}$

$\large\rm{Let\:the\:exterior\:angle\:be\:2x}$

$\large\rm\bold{\boxed{I\:=\:\frac{(n-2)180}{n}}}$

$\large\rm{I\rightarrow{Interior\:angle\:of\:regular\:polygon}}$

$\large\rm{n\rightarrow{Number\:of\:sides\:of\:polygon}}$

$\large\rm{\implies{\frac{(n-2)180}{n}\:=\:3x}}$

$\large\rm{\implies{\frac{(n-2)180}{3n}\:=\:x--eq(1)}}$

$\large\rm\bold{\boxed{E\:=\:\frac{360}{n}}}$

$\large\rm{E\rightarrow{Exterior\:angle\:of\:Regular\:polygon}}$

$\large\rm{n\rightarrow{Number\:of\:sides\:of\:polygon}}$

$\large\rm{\implies{2x\:=\:\frac{360}{n}}}$

$\large\rm{\implies{x\:=\:\frac{360}{2n}---eq(2)}}$

$\large\rm{In\:Both\:Equations\:RHS\:Can\:be\:equated}$

$\large\rm{\implies{\frac{(n-2)180}{3n}\:=\:\frac{360}{2n}}}$

$\large\rm{\implies{60(n-2)\:=\:\frac{180}{n}}}$

$\large\rm{\implies{n-2\:=\:\frac{3}{n}}}$

$\large\rm{\implies{n^2-2n\:=\:3}}$

$\large\rm{\implies{n^2-2n-3\:=\:0}}$

$\large\rm{\implies{n^2+n-3n-3\:=\:0}}$

$\large\rm{\implies{n(n+1)-3(n+1)\:=\:0}}$

$\large\rm{\implies{(n+1)(n-3)\:=\:0}}$

$\large\rm{\implies{n\:=\:-1\:(or)\:n\:=\:3}}$

$\large\rm{n\:=\:-1\:is\:not\:possible\:because\:sides\:of\:Regular\:polygon\:is\:never\:negative}$

$\large\rm{\therefore{The\:Number\:of\:sides\:=\:3}}$

Answer 2

Answer:

no of side is 3

Step-by-step explanation:

tq for points