Correct Answer - Option 3 : 1080°
Calculation:
Interior angle of polygon A = (m - 2) × 180/m
Interior angle of polygon B = (n - 2) × 180/n
Then,
⇒ (m - 2) × 180/m = 3/5 × (n - 2) × 180/n
⇒ (m - 2)/m = 3/5 × (3m - 2)/3m
⇒ 5m - 10 = 3m - 2
⇒ m = 4
⇒ n = 4 × 3 = 12
Number of sides of polygon (n - m) = 12 - 4 = 8 sides
Interior angle of 8 sided regular polygon = (8 - 2) × 180/8 = 135°
∴ Sum of interior angles of 8 sided regular polygon = 135 × 8 = 1080°
Let n = side of regular polygon
Interior angle of n sided regular polygon = (n - 2) × 180°/n
Sum of n sided regular polygon = (n - 2) × 180°