Question

In a regular polygon each interior angle is 140 degrees greater than each exterior angle. Find the number of sides

Answer 1

Answer:

Each interior angle of a regular polygon = 140 deg. So each exterior angle of the regular polygon = 180-140 = 40 deg. Hence the regular polygon has 360/40 = 9 sides.

Answer 2

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ number \ of \ sides \ is \ 18.}$

$\sf\orange{Given:}$

$\sf{\implies{In \ a \ regular \ polygon \ each \ interior}}$

$\sf{angle \ is \ 140° \ greater \ than \ each \ exterior \ angle.}$

$\sf\pink{To \ find:}$

$\sf{The \ number \ of \ side \ of \ the \ polygon.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ exterior \ angle \ of \ polygon \ be \ x.}$

$\sf{\therefore{Interior \ angle=x+140}}$

$\sf{According \ to \ the \ linear \ pair \ axiom}$

$\sf{x+(x+140)=180}$

$\sf{\therefore{2x+140=180}}$

$\sf{\therefore{2x=180-140}}$

$\sf{\therefore{2x=40}}$

$\sf{\therefore{x=\frac{40}{2}}}$

$\boxex{\sf{\therefore{x=20}}}$

$\sf{\therefore{All \ exterior \ angle=20°}}$

$\sf{Number \ of \ sides=\frac{360}{Exterior \ angle}}$

$\sf{\therefore{Number \ of \ sides=\frac{360}{20}}}$

$\sf{\therefore{Number \ of \ sides=18}}$

$\sf\purple{\tt{\therefore{The \ number \ of \ sides \ is \ 18.}}}$