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Quadrilateral PQRS is shown.

There is a quadrilateral PQRS in which the length of side PQ is 6b, the length of side QR is 4a+1, the length of side RS is 11b-10, and the length of side PS is 2a+9. The measure of angle PQR is (6x+13) degrees and the measure of angle PSR is (7x-5) degrees.

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

Answer :

Answer:

The value of a = 8  and b= 2  for PQRS to be a parallelogram  

Step-by-step explanation:

Given as :

Quadrilateral PQRS having side PQ , QR , RS , PS

The measure of side is

PQ = 6b ,           QR = 4a + 1

RS =  11b - 10    , PS = 2a + 9

The measure of angle PQR is  (6x + 13)    And   PSR is  (7x - 5)

The parallelogram become quadrilateral  when its opposite sides is parallel and equal

I.e PQ = RS            And           QR = PS

Or 6b = (11b - 10)    

Or, 10 = 11b - 6b      

Or, 5b = 10

∴  b= [tex]\frac{10}{5}[/tex] = 2      or, b = 2

Again ∵  QR = PS

So,  4a + 1 = 2a + 9

Or,   4a - 2a = 9 - 1

∴   a = 8

Hence the value of a = 8  and b= 2  for PQRS to be a parallelogram  Answer

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