Question

find the number of sides of a regular polygon if its interior angle is(4\pi /5)^c

Answer 1

Answer:

$\sf{The \ number \ of \ sides \ of \ a \ regular \ polygon \ is \ 10.}$

Given:

$\sf{Interior \ angle \ of \ a \ regular \ polygon=(\dfrac{4\pi}{5})^{c}}$

To find:

$\sf{Number \ sides \ of \ a \ regular \ polynomial.}$

Solution:

$\sf{Interior \ angle =(\dfrac{4\pi}{5})^{c}} \\ \\ \sf{\therefore{Interior \ angle=(\dfrac{4\pi}{5}\times\dfrac{180}{\pi})^\circ}} \\ \\ \sf{\therefore{Interior \ angle=144^\circ}} \\ \\ \sf{Interior \ angle + Exterior \ angle=180^\circ} \\ \\ \sf{\therefore{Exterior \ angle=180^\circ-144^\circ}} \\ \\ \sf{\therefore{Exterior \ angle=36^\circ}} \\ \\ \\ \sf{Note: \ [ \ For \ regular \ polygon,} \\ \\ \sf{Number \ of \ sides=\dfrac{360}{Exterior \ angle} \ ]} \\ \\ \\ \sf{\therefore{Number \ of \ sides=\dfrac{360}{36}}} \\ \\ \sf{\therefore{Number \ of \ sides=10}} \\ \\ \purple{\tt{The \ number \ of \ sides \ of \ regular \ polygon \ is \ 10.}}$