SOLUTION: Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of X and Y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees &

Algebra ->  Parallelograms -> SOLUTION: Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of X and Y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees &      Log On


   

Question 589326: Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of X and Y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees ∠B is (2x-3y) degrees ∠C is (4x) degrees and ∠D is (2x-5y) degrees. There is also an exterior angle that extends from ∠D and that exterior angle is (6x+2y) degrees. Once again the question asks to solve for X and Y, and the shape if the figure is a rhombus. I hope this a good enough explanation that someone's able to help. Thank you.
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of x and y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees ∠B is (2x-3y) degrees ∠C is (4x) degrees and ∠D is (2x-5y) degrees. There is also an exterior angle that extends from ∠D and that exterior angle is (6x+2y) degrees. Once again the question asks to solve for X and Y, and the shape if the figure is a rhombus. I hope this a good enough explanation that someone's able to help. Thank you.


Opposite angles of a rhombus have equal measures, so

             m∠A = m∠C

            4x-y = 4x

             m∠B = m∠ADC

           2x-3y = 2x-5y

The two angles at D are supplementary, so

  m∠ADE + m∠ADC = 180°

(6x+2y) + (2x-5y) = 180


(1)              4x-y = 4x
(2)             2x-3y = 2x-5y
(3)   6x+2y + (2x-5y) = 180

Simplifying equation (1)

(1)              4x-y = 4x
                   -y = 0
                    y = 0

Substituting y = 0 in (2) and (3)

(2)             2x-3·0 = 2x-5·0
(3)   6x+2·0 + (2x-5·0) = 180

(2)                  2x = 2x
(3)           6x + (2x) = 180

Solving (3)

                    8x = 180
                     x = 22.5°

So the rhombus is really a square.

Edwin