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Math Help - Trapezoid Conundrum =/

  1. #1
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    Question Trapezoid Conundrum =/

    Trapezoid CART has median Line BD.

    If the measure of angle C and the measure of angle R =140, find the measure of angle T and angle A.

    If TB = 10 and DA = 17, find BC and RD.

    If TR = 2x-5, BD = x+4, and CA = 4x-3, find x.

    I'm so very confused =/...Please explain how to get to the answer! Thanks so much for any help!
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by lprox015 View Post
    Trapezoid CART has median Line BD.

    If TB = 10 and DA = 17, find BC and RD.
    Are you saying that the measure of (C + R) = 140? If so, then since any the total of the angles of any quadrilateral is 360, the measure of (T + A) = 360 - (C + R) = 360 - 140 = 220.
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  3. #3
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by lprox015 View Post
    Trapezoid CART has median Line BD.

    If TB = 10 and DA = 17, find BC and RD.
    If BD is a median line, then BD bisects TC and RA, so TB = BC = 10 and DA = RD = 17.
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  4. #4
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    Quote Originally Posted by lprox015 View Post
    Trapezoid CART has median Line BD.
    ...
    If TB = 10 and DA = 17, find BC and RD.

    If TR = 2x-5, BD = x+4, and CA = 4x-3, find x....
    Hello,

    the length of the median line is the average of the length of the two parallels:

    BD = (TR + CA)/2. That means:

    x+4 = (2x-5 + 4x-3)/2 = (6x-8)/2 = 3x-4

    -2x = -8

    x = 4
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