Faiza A.

asked • 02/28/22

a=2 b=4 please corect me if i am wrong

Quadrilateral PQRS is shown.


Quadrilateral P Q R S. Side P Q has length 6 b, side Q R has length 4 a plus b, side R S has length 11 b minus 10 a, and side S P has length 2 a plus 8. Angle P Q R has measure 6 x plus 13 degrees and opposite angle R S P has measure 7 x minus 5 degrees.


What must the values of a and b be for PQRS to be a parallelogram?


a = 


b = 


Brenda D.

tutor
Sorry but I do have a couple of questions. Did you simply substitute your values in the expressions above to check or did you just want them confirmed as they are below? Your numbers are correct did you need to know why?
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03/01/22

3 Answers By Expert Tutors

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Jon S. answered • 03/01/22

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Opposite sides of a parallelogram are equal so


2a + 8 = 4a + b

6b = 11b - 10a


putting in correct form for simultaneous equations:

2a + b = 8

10a -5b = 0


multiply 1st equation by 5:

10a + 5b = 40

10a - 5b = 0


add two equations

20a = 40

a = 2


substitute value of a into equation 2a + b = 8

2(2) + b = 8

b = 4


as far as for x, opposite angles of a parallelogram are equal so:

6x + 13 = 7x - 5

18 = x

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