A polygon has n sides. Three of its exterior angels are 70 degrees, 80 degrees and 90 degrees. The remaining ( n - 3 ) exterior angels are each 15 degrees. How many sides does this polygon have?

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A polygon has n sides. Three of its exterior angels are 70 degrees, 80 degrees and 90 degrees. The remaining             (      n      -      3      )       exterior angels are each 15 degrees. How many sides does this polygon have?

Zackary Hatfield · Accepted Answer

Step 1Sum of the exterior angles of any polygon is always             360      ∘      As three angles are             70      ∘        ,          80      ∘       ,             70      ∘        ,          80      ∘       and             90      ∘       and remaining       n    -    3   angles are             15      ∘       and their sum is             360      ∘       , we have      70    +    80    +    90    +    15          (      n      -      3      )        =    360  or       15          (      n      -      3      )        =    360    -    70    -    80    -    90    =    120  and       n    -    3    =          120      15        =    8  i.e.       n    =    11  Hence, polygon has 11 sides

A polygon has n sides. Three of its exterior angels are 70 degrees, 80 degrees and 90 degrees. The remaining (n-3) exterior angels are each 15 degrees. How many sides does this polygon have?

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