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

Given: In Hexagon ABCDEF

AB || FE

and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3

Let ∠B = 6x,  ∠C = 4x, ∠D = 2x,  ∠E = 3x

Now AB || FE and AF is the transversal

⇒ ∠A + ∠F = 180°  (Linear pair)

Now Hexagon has 6 sides

⇒ Sum of angles of hexagon = (6 – 2) × 180°

⇒ ∠A + ∠B + ∠C + ∠D + ∠E + ∠F  = 4 × 180°

⇒ 180° + 6x + 4x + 2x + 3x = 720°

⇒ 15x = 720° – 180°

Hence ∠B  = 6 × 36° = 216°

and ∠D  = 2 × 36° = 72°