SWAG
  • SWAG
What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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experimentX
  • experimentX
(n-2)*180/n = 180 - 72, find n, then your sum is (n-2)*180
ash2326
  • ash2326
Sum of interior and exterior angle is 180 so \[Interior\ angle\ = 180-72=108\] Now we need to find the no of sides of the polygon= n We know that interior angle of n-sides is given by \[\frac{(n-2)\times 180}{n}\] We have \[(n-2)\times 180=108n\] or \[180n-360=108n\] or \[72n=360\] n=5 sides so there are 5 angles each of 108 degrees Sum of the interior angles=108+108+108+108+108=540

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