SOLUTION: parellelogram abcd has a diagonal of ac angle cab is x-12 angle acd is 1/2y angle d is 4x-8 angle b is 3y-4 please help!

Question 179885: parellelogram abcd has a diagonal of ac
angle cab is x-12
angle acd is 1/2y
angle d is 4x-8
angle b is 3y-4
please help!
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
parellelogram abcd has a diagonal of ac
angle cab is x-12
angle acd is 1/2y
angle d is 4x-8
angle b is 3y-4
please help!
:
we know because this is a parallelogram that cab is = to acd
and we know that angle d is equal to angle b
:
x-12=1/2y...........eq 1
4x-8=3y-4...........eq 2--->4x-3y=4
:
multiply all terms in eq 1 by 2 to get rid of fraction
:
2x-24=y--->2x-y=24
:
2x-y=24....eq 1 revised
4x-3y=4....eq 2 revised
:
muliply eq 1 by -3 and add both equations together
:
-6x+3y=-72...eq 1 revised
4x-3y=4......eq 2 revised
:
adding the terms in each equation and the y term is eliminated becaue +3y-3y=0
we are left with -6x+4x=-72+4
:
-2x=-68
:

:
take x's found value and plug it into any numbered equation above. I choose eq 1 revised
:
2(34)-y=24--->-y=-44-->
:
angle cab is x-12---->34-12=22 degrees
angle acd is 1/2y---->1/2(44)=22 degrees
angle d is 4x-8------>4(34)-8=128 degrees
angle b is 3y-4------>3(44)-4=128 degrees
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