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geometry

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Lines M and T are parallel with a Transversal line P. [Labeling for the angles on line P intersecting M are, top right corner is angle 1, the top left is angle 2, the bottom left is angle 3, and the bottom left is angle 4. This pattern {top left, top right, bottom left, bottom right} is the same for line P intersecting through line T, however the angle numbers are angles 5 to 8.] (exterior angles are 1, 2, 7, and 8. interior angles are 3, 4, 5, and 6)

I know that M<1=5x-16 and M<8=2x+32. I must find all 8 angles in DEGREE form. However i do not know how to do that.

  • geometry -

    You know ∠5 + ∠8 = 180
    ∠5 = 180 - (2x+32) = 148-2x

    you also know that ∠1 = ∠5
    5x - 16 = 148 - 2x
    7x = 164
    x = 164/7° --- I would would have expected the answer to come out "nicer".

    So angle 1 = 5x-16 = 5(164/7) - 16 = 708/7

    check my arithmetic, then carefully calculate the other angles.

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