Question 175245: The interior angles of a polygon have measures 170 degrees, 160 degrees, 150 degrees, 140 degrees... down to some smallest angle. The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression. Find the number of sides of the polygon.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The interior angles of a polygon have measures 170 degrees, 160 degrees, 150 degrees, 140 degrees... down to some smallest angle. The numbers 170 degrees, 160 degrees, 150 degrees, 140 degrees are members of an Arithmetic Progression. Find the number of sides of the polygon.
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The sum of the exterior angles is 360.
Each exterior angle is the supplement of an interior angle.
The angles exterior to the listed interior angles are:
10,20,30,40, etc.
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Equation:
10 + 20 + 30 + 40 + x = 360
x = 260
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Find the arithmetic sequence 50+60+70+80 = 260
Since there are 8 exterior angles, there are 8 sides.
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Cheers,
Stan H.
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