anonymous
  • anonymous
The measure of each interior angle is twice the measure of an exterior angle, how may sides does the regular polygon have?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Mertsj
  • Mertsj
6
Mertsj
  • Mertsj
The sum of the exterior angles of a regular polygon is 360. If the polygon has n sides, each exterior angle is 360/n. The problem says that the interior angle is twice the exterior angle but the interior angle is supplementary to the exterior angle. So the interior angle is 180-360/n. And so:
Mertsj
  • Mertsj
\[2(\frac{360}{n})=180-\frac{360}{n}\]

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Mertsj
  • Mertsj
n is the number of sides, by the way.
Directrix
  • Directrix
In the regular polygon, an interior angle and an exterior angle form a linear pair.|dw:1332877003562:dw|
Directrix
  • Directrix
Let exterior angle be x Then, interior angle is 2x. x + 2x = 180 3x = 180 x = 60 ----> Exterior Angle 2x = 120 --> Interior Angle The sum of the exterior angles of a convex polygon is 360. So, if each one has measure 60 and the sum is 360, then there are this many exterior angles:--> 360/60 = *6*. If there are 6 exterior angles, there are 6 interior angles, and 6 sides for the polygon. It is a regular hexagon.

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