SOLUTION: How many sides would a regular polygon have if each interior angle measures 162�? A. 10 B. 12 C. 18 D. 20

Question 530202: How many sides would a regular polygon have if each interior angle measures 162�?
A. 10
B. 12
C. 18
D. 20
Found 2 solutions by oberobic, MathTherapy:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The total interior degrees of polygon = (n-2)*180, n = number of sides.
Note that 'n' also define the number of interior angles.
Think about it: a triangle has 3 sides and 3 interior angles, a pentagon has 5 and 5, etc.
.
Divide the total interior angles by the number of angles, which will equal 162 degrees (as is given).
.
(n-2)*180 /n = 162
.
180n - 360 = 162n
.
18n = 360
.
n = 20 sides, which means there will 20 angles, too.
.
Check the answer.
.
(n-2)*180 = 18*180 = 3240 degrees
.
3240/20 =162 degrees
.
Done.
Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!
How many sides would a regular polygon have if each interior angle measures 162�?
A. 10
B. 12
C. 18
D. 20

Amount of sides of a regular polygon can be found by dividing the total degrees of the exterior angles, 360, by the amount of degrees of one exterior angle.

In this case, each exterior angle = 180 - 62, or , so we get: , or sides.

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