Question

If one of the internal angle of a regular polygon is 135°, Then find the number of diagonals in the polygon.
1. 16
2. 18
3. 20
4. 24

Answer 1

Correct Answer - Option 3 : 20

Given

One of the internal angles of a regular polygon is 135°

Concept

Each interior angle of a regular polygon = [(n -2)/n] × 180° 

Number of diagonals = [n(n - 3)/2] 

Calculation

⇒ 135° = [(n -2)/n] × 180°  

⇒ (135°/180°) = [(n -2)/n]

⇒ (3/4) = [(n -2)/n]

⇒ 3n = 4n - 8

⇒ n = 8

Now, we get

⇒ Number of diagonals = 8(8 - 3)/2

⇒ Number of diagonals = 20 

∴ Number of diagonals is 20