Question

If each interior angle of a regular polygon is 10 times its exterior angle ,then the number of sides the polygon has?

Answer 1

Regular polygon has `22` sides.

Explanation:

Let `n` be the number of sides regular polygon.

Exterior angle is `A_e = 360/n`

Interior angle is `A_i = (n-2)/n*180`

By given condition : `A_i=10*A_e`

`:. 10*360/canceln= (n-2)/cancel n*180` or

`3600= (n-2)*180 or n-2 = 20 :. n= 22`

Regular polygon has `22` sides. [Ans]

Answer 2

`22`

Explanation:

`"using the following polygon facts"`

`• "interior angle + exterior angle "=180^@`

`• " sum of exterior angles "=360^@`

`rArr"number of sides "n=360^@/"exterior angle"`

`"let x be the exterior angle"`

`rArr"interior angle "=10x`

`rArr11x=180rArrx=180/11`

`rArrn=360/(180/11)=cancel(360)^2xx11/cancel(180)^1=22`