Answer: The value of x is 20° and the measurement of angle B is 150°.
Step-by-step explanation: Given that the angle measurements in the figure are represented by the following expressions :

We are to solve for the value of x and then for the measurement of angle B.
We can see in the figure that
the two lines are parallel and they cut by a transversal.
Therefore,
![m\angle A=m\angle B~~~~~~~~~~~~~~~\textup{[alternate interior angles]}\\\\\Rightarrow 8x-10^\circ=3x+90^\circ\\\\\Rightarrow 8x-3x=90^\circ+10^\circ\\\\\Rightarrow 5x=100^\circ\\\\\Rightarrow x=(100^\circ)/(5)\\\\\Rightarrow x=20^\circ.](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ponacflsxo8n9o5zafzelhyhigsv2g6s7h.png)
And, the measurement of B will be

Thus, the value of x is 20° and the measurement of angle B is 150°.