Question

ABCDE is a pentagon in which AB || DC and angle A = 120°. If angleD: angle E = 3:5 find angle d​

Answer 1

Answer:

Correct option is D)

In a pentagon ABCDE, AB is parallel to DC and ∠A:∠E:∠D=3:4:5  

So, ∠B+∠C=180  

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

Let ∠A=3x,∠E=4x,∠D=5x

Sum of all interior angles of pentagon = 180  

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(n−2)=180  

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(5−2)=540  

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Now,

∠B+∠C+∠A+∠E+∠D=540  

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=>180  

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+3x+4x+5x=540  

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=>12x=360  

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=>x=30  

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∠E=4x=4×30  

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=120  

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Step-by-step explanation: