anonymous
  • anonymous
The measure of each exterior angle of a regular polygon is 2/3 that of an interior angle. How many sides does the regular polygon have?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Make sure you explain how you get your answer.
.Sam.
  • .Sam.
Interior angle\[=\frac{(n-2)*180}{n}\] Sum of all exterior angles=360 Angles of each exterior angle \[=\frac{360}{n}\] So, Angles of each exterior angle=2/3 Interior angle \[\frac{360}{n}=\frac{2}{3}*\frac{(n-2)*180}{n}\] n=5
.Sam.
  • .Sam.
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Directrix
  • Directrix
Let x be the measure of the interior angle Then, (2/3) x is the measure of the adjacent exterior angle. x + (2/3)x = 180 (5/3)x = 180 x = 108 which is the measure of one interior angle The adjacent exterior angle is 180 - 108 = 72. You could crank out the 72 by taking (2/3) of 108. The key here is knowing that the sum of the exterior angles is 360. 360 divided by 72 gives 5 which means there are 5 exterior angles, 5 interior angles, and 5 sides. This is a regular pentagon.

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