The diagram shows two parallel lines cut by a transversal. If the measure of ∠3=(2y+20)∘ and the measure of ∠5=(210−4y)∘, what is the measure of ∠4 ?

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∠4 = 110

Step-by-step explanation:

∠3 + ∠5 = 180    {Co-interior angles are supplementary}

2y + 20 + 210 - 4y = 180

2y - 4y + 20 + 210 = 180    {Combine like terms}

-2y + 230 = 180

Subtract 230 from both sides

-2y = 180 - 230

-2y = -50  

Divide both sides by (-2)

  y = -50/-2

y = 25

∠5 = 210 - 4y

      = 210 - 4*25

       = 210 - 100

∠5 = 110

∠4 = ∠5    {Alternate interior angles are equal}

∠ 4 = 110°

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step-by-step explanation: