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Given quadrilateral ABCD, with A = 4x - 57 and C = x + 3, what value of x ensures that ABCD is a parallelogram?

  • geometry -

    recall the properties of parallelogram,,
    one of the properties of a parallelogram is that the opposite angles are congruent/equal,, since you are given angles A and C, and they are opposite, equate them to get x:
    4x - 57 = x + 3
    combining similar terms,
    4x - x = 57 + 3
    *when transposing terms to other side of equation, the sign becomes the opposite,, that's why x (from right side) when transposed to left side becomes -x, and -57 becomes 57 after transposing,, simplifying this,
    3x = 60
    x = 20

    hope this helps. :)

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