Question

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

Answer 1

Given: Hexagon ABCDEF in which AB || EF and ∠B : ∠C : ∠D : ∠E = 6 : 4 : 2 : 3.

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°

Ratio = 6: 4: 2: 3

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

∴ ∠B = `6/15 xx 540 = 216^circ`

∠D = `2/15 xx 540^circ = 72^circ`

Hence ∠B = 216° ; ∠D = 72°