In a regular polygon each interior angle is 135 ∘ greater than each exterior angle. How many sides has the polygon?

Question

In a regular polygon each interior angle is       135          ∘       greater than each exterior angle. How many sides has the polygon?

jennasyliang4tr · Accepted Answer

Step 1Exterior angle of regular polygon of n sides is       E    =          360      n      Interior angle of regular polygon of n sides is       I    =                  180                  (          n          -          2          )                    n      Given condition,       I    =    E    +    135    ∴                  180                  (          n          -          2          )                    n        =          360      n        +    135   or                     180                  (          n          -          2          )                    n        -          360      n        =    135   . Multiplying by n on both sides we get,       180          (      n      -      2      )        -    360    =    135    n   or       180    n    -    360    -    360    =    135    n                or              180    n    -    135    n    =    720   or       45    n    =    720                or              n    =          720      45                    or              n    =    16  The polygon is Hexakaidecagon having 16 sides.

In a regular polygon each interior angle is 135^circ greater than each exterior angle. How many sides has the polygon?

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