If each interior angle of a regular polygon is 135 deg then the number of diagonals of the polygon i...........

Quantitative Aptitude (CDS) Geometry

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If each interior angle of a regular polygon is 135°, then the number of diagonals of the polygon is equal to

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Explanation:

Let the number of sides of the polygon be n
Formula:
Each interior angle of the regular polygon =(n-2) x 180⁰/n
(n-2) x 180⁰/n=135^{o

=> 180n - 135n=360

=> n=8}
The number of vertices of the polygon = The number of sides of the polygon = n = 8
Formula:
The number of diagonals of the polygon of side n=n(n-3)/2
The number of diagonals of the polygon of side 8=8 x 5/2=20