Question

If each interior angle of a regular polygon is 135 degree then the number of diagonals of the polygon is equal to (1) 54 (2)48(3)20(4)18

Answer 1

Hello Dear.

Here is the 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.


Hope it helps.

Answer 2

Sum of the interior angles of a regular
Polygon of " n " sides is (n-2)×180

That is
n × 135 = (n -2)× 180

3n = (n - 2) × 4

3n = 4n - 8

n = 8.

Therefore the given polygon has 8 sides.

The number of diagonals of a polygon of n sides

= n(n-3)/2

= 8× 5/2

= 20