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Math Help - Parallelograms & Quadrilaterals

  1. #1
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    Parallelograms & Quadrilaterals

    Hey Guys!

    For NUMBER 9)


    I'm trying to find the answer but I don't know how to set up this equation.

    Since Angle A = Angle C

    I am setting up the equation as 2x/3 = x/2 + 20

    I take out the fractions with 6 and I get 4x = 3x + 20
    then I get x = 20

    Doesn't seem to work though. The answers are m∠A = m∠C = 80;m∠B = m∠D = 100
    Attached Thumbnails Attached Thumbnails Parallelograms & Quadrilaterals-screen-shot-2013-10-26-7.38.03-pm.png  
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  2. #2
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    Re: Parallelograms & Quadrilaterals

    Hey Cake.

    Are you assuming your shape is a parallelogram (or a rhombus)? If so then you can use the fact that angle A = angle C and angle B = angle D where total sum of angles is 360.

    So basically you have 2*angle(A) + 2*angle(B) = 360 where

    2x/3 = x/2 + 20
    4x = 3x + 120 (multiply everything by 6)
    x = 120

    This implies angle(A) = angle(C) = 2*120/3 = 80.

    Since 2*angle(A) + 2*angle(B) = 360 you have angle(B) = (360 - 2*80)/2 = angle(D) = 100.
    Thanks from Cake
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  3. #3
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    Re: Parallelograms & Quadrilaterals

    I see now.

    so angle B is basically (360 - 2(angle A or C, which is 80)) then you divide by 2?

    Sorry, why do you divide by two? Is it because there are two angles (angle B and D)?
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  4. #4
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    Re: Parallelograms & Quadrilaterals

    Basically because the angle is equal to its opposite. In other words B = D and A = C (in terms of angles) of the interior of the rhombus.

    I divide by two because you have a factor of 2 in front of the variables. I have 2x = blah so I need to use 2x/2 = blah/2 = x to solve for x.
    Thanks from LimpSpider and Cake
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  5. #5
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    Re: Parallelograms & Quadrilaterals

    Quote Originally Posted by Cake View Post
    I am setting up the equation as 2x/3 = x/2 + 20

    I take out the fractions with 6 and I get 4x = 3x + 20
    then I get x = 20
    Should be: 4x = 3x + 120 ; ok?
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  6. #6
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    Re: Parallelograms & Quadrilaterals

    Quote Originally Posted by chiro View Post
    Basically because the angle is equal to its opposite. In other words B = D and A = C (in terms of angles) of the interior of the rhombus.

    I divide by two because you have a factor of 2 in front of the variables. I have 2x = blah so I need to use 2x/2 = blah/2 = x to solve for x.
    Perfect, thanks.
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