One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?

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One exterior angle of a regular polygon measures 36. What is the sum of the polygon&#039;s interior angle measures?

Nigerkamg5 · Accepted Answer

Step 1In the diagram above, let your exterior angle be 36. Now your interior angle and exterior angle with the line extended add to equal to 180 degrees since the line drawn is a straight line. Therefore, if one exterior angle of the regular polygon is 36, then the interior angle is       180    -    36    =    144  The angle sum of any polygon is given by       180          (      n      -      2      )       where n is the number of sides of the polygonTherefore, the angle sum of the polygon is equal to the one interior angle multiplied by the number of angles there are. Now since the number of angles is equivalent to the number of sides, we can write it like this:      180          (      n      -      2      )        =    144    n        180    n    -    360    =    144    n        36    n    =    360        n    =    10  Since the polygon has 10 sides, then it must be a decagon.Now, putting       n    =    10   back into the equation       180          (      n      -      2      )       gives:      180          (      10      -      2      )        =    180    ×    8    =    1440

Alberto Calhoun · Accepted Answer

Step 1Let the number of sides of regular polygon be nExterior angle of regular polygon is       E    =          360      n        ;    E    =          36      0            ∴    n    =          360      E        =          360      36        =    10   . So it is regular Decagon having 10 equal sides. Sum of polygon&#039;s interior angles is      ∑    i    =          (      n      -      2      )        ⋅    180    =          (      10      -      2      )        ⋅    180    =          1440      0

One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?

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