SOLUTION: . Find the number of sides of a regular polygon if each interior angle measures 162°. The number of sides is: A. 20 B. 16 C. 24 D. 18

Algebra ->  Polygons -> SOLUTION: . Find the number of sides of a regular polygon if each interior angle measures 162°. The number of sides is: A. 20 B. 16 C. 24 D. 18       Log On


   

Question 709179: . Find the number of sides of a regular polygon if each interior angle measures 162°. The number of sides is:
A. 20
B. 16
C. 24
D. 18

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
(n-2)*180, how many degrees for sum of measures of the interior angles.
(n-2)*180/n, how may degrees in one interior angle because the polygon has n angles.

highlight%28%28n-2%29%2A180%2Fn=162%29
Find n.

180 and 162 are divisible by 18.
This then is equivalent: %28n-2%29%2A10%2Fn=9
(n-2)10=9n
10n-20=9n
n=20