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 # 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]

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#