Question

In a hexagon ABCDEF, side AB|| side FE and angle B:angle C: angle D: angle E = 6:4:2:3 find angle B and angle D​

Answer 1

Answer:

ANSWER

In a hexagon ABCDEF, side AB is parallel to side FE.

∠A+∠F=180

o

(Sum of interior angles on the same side of the transversal is supplementary).

∠B:∠C:∠D:∠E=6:4:2:3

Let ∠B=6x,∠C=4x,∠D=2x,∠E=3x

Sum of interior angles of hexagon = 180

o

(n−2)=180

o

(6−2)=720

o

(where n = number of sides of polygon )

Now,

∠A+∠F+∠B+∠C+∠D+∠E=720

o

180

o

+6x+4x+2x+3x=720

o

15x=540

o

x=36

o

∠B=6x=6×36

o

=216

o

∠D=2x=2×36

o

=72

o

∠C=4x=4×36

o

=144

o

∠E=3x=3×36

o

=108

o

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Answer 2

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HERE IS UR ANSWER

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Hexagon ABCDEF in which AB  ∥ EF

Hexagon ABCDEF in which AB  ∥ EFAnd ∠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° = 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°