SOLUTION: A regular polygon has n sides. The ratio of its interior angle to its exterior angle is 7:2. Calculate the size of each interior angle and the value of n.

Algebra ->  Polygons -> SOLUTION: A regular polygon has n sides. The ratio of its interior angle to its exterior angle is 7:2. Calculate the size of each interior angle and the value of n.      Log On


   

Question 212080: A regular polygon has n sides. The ratio of its interior angle to its exterior angle is 7:2. Calculate the size of each interior angle and the value of n.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Let 7a=interior angle
2a=exterior angle
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7a+2a=180
9a=180
a=20
So,
2a=40
7a=140
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For a regular polygon of n sides, each exterior angle has a measure of 360/n degrees.
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The measure of each interior angle is 140 degrees
Since the exterior angle of each angle has measure 40 degrees, then the number of sides n=360/40=9 sides.