We are given m<PXQ = (8x-3).
m<PXS = (10x+30).
According to given diagram, it is shown that m<PQX = m<QXS.
Therefore, < m<QXS= (8x-3).
We also can see that Sum of angles m<PQX and m<QXS equals m<PXS.
Therefore, we can setup an equation.
m<PQX + m<QXS = m<PXS.
(8x-3) + (8x-3)= (10x+30)
8x-3 +8x -3 = 10x +30.
Combining like terms, we get
8x+8x -3-3 = 10x +30
=> 16x -6 = 10x +30.
Adding 6 on both sides
16x -6+6 = 10x +30+6
16x = 10x +36.
Subtracting 10x from both sides, we get
16x-10x = 10x-10x +36
6x= 36.
Dividing both sides by 6, we get
6x/6= 36/6
x=6.
Now, we need to find the value of m<QXS.
m<QXS = 8x-3.
plugging x=6.
m<QXS = 8(6)-3 = 48-3 = 45.
m<QXS = 45 degrees.
Therefore, x=6 and m<QXS = 45 degrees.