Question

The angle measurements in the diagram are represented by the following expressions

Answer 1

8x-10=3x+90
5x=100
X=20
B=3(20)+90=150

Answer 2

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 :

$m\angle A=8x-10^\circ,~~~m\angle B=3x+90^\circ.$

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,

$m\angle A=m\angle B~~~~~~~~~~~~~~~\textup{[alternate interior angles]}\\\\\Rightarrow 8x-10^\circ=3x+90^\circ\\\\\Rightarrow 8x-3x=90^\circ+10^\circ\\\\\Rightarrow 5x=100^\circ\\\\\Rightarrow x=\dfrac{100^\circ}{5}\\\\\Rightarrow x=20^\circ.$

And, the measurement of B will be

$m\angle B=3x+90^\circ=3\times 20^\circ+90^\circ=60^\circ+90^\circ=150^\circ.$

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