Answer: [tex]m\angle B=70\°[/tex]
Step-by-step explanation:
By definition, the sum of the interior angles of a triangle is 180 degrees.
Based on this, you need to set up the following equation:
[tex]40+(2x-30)+(x+20)=180[/tex]
The next steo is to solve for "x" in order to find its value. This is:
[tex]40+2x-30+x+20=180\\\\30+3x=180\\\\3x=180-30\\\\3x=150\\\\x=\frac{150}{3}\\\\x=50[/tex]
You can observe in the picture of the triangle ABC given in the exercise, that:
[tex]m\angle B=(2x-30)\°[/tex]
Therefore, you must substitute the value of "x" into that equation and then evaluate, in order to find the measure of the angle B. This is:
[tex]m\angle B=(2(50)-30)\°\\\\m\angle B=(100-30)\°\\\\m\angle B=70\°[/tex]
