Question

Quadrilateral PQRS is shown.

Answer 1

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= $\frac{10}{5}$ = 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