Find the value of 'x' and m < qxs

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.