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

2 Answers
Aug 27, 2017

Regular polygon has 22 22 sides.

Explanation:

Let nn be the number of sides regular polygon.

Exterior angle is A_e = 360/n Ae=360n

Interior angle is A_i = (n-2)/n*180 Ai=n2n180

By given condition : A_i=10*A_e Ai=10Ae

:. 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]

Aug 27, 2017

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