in a hexagon ABCDEF, side AB is a parallel to EF and angle B : angle C : angle D : angle E = 5 : 4 : 2 : 1. find angle b, c, d and e
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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
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(n−2)=180
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(6−2)=720
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(where n = number of sides of polygon )
Now,
∠A+∠F+∠B+∠C+∠D+∠E=720
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180
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+6x+4x+2x+3x=720
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15x=540
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x=36
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∠B=6x=6×36
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=216
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∠D=2x=2×36
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=72
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∠C=4x=4×36
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=144
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∠E=3x=3×36
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=108
o
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Answer:
Step-by-step explanation:
B = 24 , C = 30 , D = 60 , E = 120.
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