In a hexagon ABCDEF, side AB is parallel to side FE and B:C:D:E=6:4:2:3.Find B and D

TO Find : ∠B and ∠D

Proof : No. of sides n = 6

∴ Sum of interior angles = (n – 2) × 180°

= (6 – 2) × 180° = 720°

∵ AB ∥ EF (Given)

∴ ∠A + ∠F = 180°

But ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720°

(Proved)

∠B + ∠C + ∠D + ∠E + ∠180 = 720°

∴ ∠B + ∠C + ∠D + ∠E = 720° – 180° = 540°

Ratio = 6 : 4 : 2 : 3

Sum of parts = 6 + 4 + 2 + 3 = 15

∴ ∠B = (6/15) × 540°= 216°

∠D = (2/15) × 540° = 72°

Hence ∠B = 216° ; ∠D = 72°

The mode of the numbers is 29.