Question

A and B be two regular polygons having m and n sides, respectively. If n = 3m and each interior angle of A is 3/5 times each interior angle of B, then sum of interior angle, in degrees, of a regular polygon with (n - m) sides is?
 
1. 108°
2. 1350°
3. 1080°
4. 135°

Answer 1

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°