Question

what is the sum of the inner angle of regular polygon is 135 .how many sides does it have​

Answer 1

Answer:

Each interior angle of the Regular Polygon = 135°

Using the Formula,

Each Interior angle of the Regular Polygon = [(n - 2) × 180] ÷ n

135° = (n - 2) × 180/n

180n - 360 = 135n

180n - 135n = 360

45n = 360

n = 360/45

n = 8

∴ Number of Sides in the Regular Polygon is 8.

Now, For Calculating the Number of Diagonals in the Polygon,

Using the Formula,

 No. of Diagonals = (n - 3)n ÷ 2

  No. of Diagonals = (8 - 3)8 ÷ 2

∴ No. of Diagonals = 5 × 4

∴ No. of Diagonals = 20.

Hence, the number of Diagonals in the Octagon is 20.

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