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°
