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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Originally Posted by lprox015

Trapezoid CART has median Line BD.

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

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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.

Quote:

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Originally Posted by lprox015

Trapezoid CART has median Line BD.

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

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If BD is a median line, then BD bisects TC and RA, so TB = BC = 10 and DA = RD = 17.

Quote:

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Originally Posted by lprox015

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....

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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