anonymous
  • anonymous
A school is designed so that 5 hallways meet at the library in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.
Mathematics
katieb
  • katieb
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mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
In this case, n = 5 = number of sides
anonymous
  • anonymous
wait how would u show ur work

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mathstudent55
  • mathstudent55
All you need to do is show two things. In a regular polygon, all angles are congruent. That means all their measures are the same. Also, in any polygon, the sum of the measures of the interior angles of a polygon is (n - 2)180, where n = number of sides. Since a pentagon has 5 sides, the sum of measures of the interior angles is (5 - 2)180 = 3(180) = 540 Since all angles are congruent, each angle is 540/5

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