Question

1. why angles of a hexagon are 122 degree 95 degree 80 degree 135 degree and 125 degree find the sixth angle ?​

Answer 1

Answer:

Sum of interior angles of a polygon with n sides = (n-2)*180

Sum of interior angles of a polygon with 6 sides(Hexagon) = (6-2)*180

                                                                                                  = 4*180

                                                                                                   =720°

Let the 6th angle be x

So,

122 + 95 + 80 + 135 + 125 + x = 720

557 + x = 720

x = 720 - 557

x = 163° ( 6th angle)

Answer 2

Given : A hexagon with angle 122,95,80,135,125.

To Find : Find the sixth angle ?

_________________________

Solution : Hexagon It is a six sided polygon. It is a closed polygon. The sum of all angles in a hexagon is 720. Hexa means six and gon means side.

$~$

$\qquad{\sf:\implies {122~ + ~95~ + ~80~ + ~135~ + ~125 ~+ ~y ~=~720}}$

$\qquad{\sf:\implies {217 ~+~ 215~ +~ 125~ +~ y~ =~ 720}}$

$\qquad:\implies{\sf{432~ +~ 125~ + ~y~ = ~720}}$

$\qquad:\implies{\sf {557~ +~ y ~=~720}}$

$\qquad:\implies{\sf {y ~= ~720~ -~ 557y}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{y ~= ~163^{ \circ}}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{The ~sixth ~angle~ of ~a~ hexagon~ is~\bf{\underline{163^{\circ}}}}}$

________________________

V E R I F I C A T I O N :

$\qquad{\rm\dashrightarrow{122 ~+ ~95~ +~ 80 ~+ ~135~ + ~125~ +~ y~ =~720}}$

$\qquad{\rm\dashrightarrow{122 ~+ ~ 95~ + ~80 ~+~ 135~ + ~125 ~+ ~163~ = ~720}}$

$\qquad{\rm\dashrightarrow{217~ + ~215~ + ~288~ = ~720}}$

$\qquad{\rm\dashrightarrow{432~ + ~288 ~= ~720}}$

$\qquad\dashrightarrow\large\pmb{\frak\red{720~ =~ 720}}$