SOLUTION: My question is:The measure of each interior angle of a regular polygon is 8 times than of an exterior angle. how many sides does a polygon have?.Thank you.

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Question 202991: My question is:The measure of each interior angle of a regular polygon is 8 times than of an exterior angle. how many sides does a polygon have?.Thank you.
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of each interior angle of a regular polygon is 8 times than of an exterior angle. how many sides does a polygon have?.
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Let the measure of the exterior angle be "x"
Then the measure of the interior angle is "8x"
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Since the two are supplementary x+8x = 180 degrees
9x = 180
x = 20 degrees (measure of each exterior angle)
8x = 160 degrees (measure of each interior angle)
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The sum of All of the exterior angles is 360 degrees.
360/20 = 18 (that is the number of exterior angles and
says the number of sides is 18)
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let I = the measure of an interior angle and E = the measure of the corresponding exterior angle.
Recall that the interior angle and the exterior angle are supplementary so: I+E = 180 degrees.
You are told in the problem that:
I = 8E "The measure of each interior angle of a regular polygon is 8 times that of an exterior angle."
Substitute I = 8E into the first equation and solve for E.
8E+E = 180
9E = 180
E = 20 Degrees. This is the measure of an exterior angle.
The interior angle is:
I = 8E
I = 8(20)
I = 160 degrees.
Now the measure of an interior angle of a regular polygon of n sides is given by:
I+=+%28n-2%29180%2Fn But we just found the measure of an interior angle: I = 160, so we substitute and solve for n.
160+=+%28n-2%29%28180%29%2Fn Multiply both sides by n.
160n+=+180n-360 Subtract 160n from both sides.
0+=+20n-360 Add 360 to both sides.
360+=+20n Finally, divide both sides by 20.
n+=+18
The regular polygon has 18 sides.