If the sum of interior angles of a regular polygon is 2340, 340. Find the number of side

Mathematics

ScanSolve AI Answer

Answer

15

Step-by-step solution

3 steps
  1. Formula for the sum of interior angles of a polygon.

    The sum of the interior angles of a polygon with nn sides is (n−2)×180∘(n-2) \times 180^\circ.

    Given sum = 2340∘2340^\circ,

    (n−2)×180∘=2340∘(n-2) \times 180^\circ = 2340^\circ
  2. Solve for n−2n-2.

    Divide both sides by 180∘180^\circ:

    n−2=2340∘180∘=13n-2 = \frac{2340^\circ}{180^\circ} = 13
  3. Solve for nn.

    n=13+2=15n = 13 + 2 = 15

    The regular polygon has 15 sides.

    15

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