Question

What is the measure of angle B in the triangle?

This triangle is not drawn to scale.

Answer 1

Answer:
`m\angle B=70\°`

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:

`40+(2x-30)+(x+20)=180`

The next steo is to solve for "x" in order to find its value. This is:

`40+2x-30+x+20=180\\\\30+3x=180\\\\3x=180-30\\\\3x=150\\\\x=(150)/(3)\\\\x=50`

You can observe in the picture of the triangle ABC given in the exercise, that:

`m\angle B=(2x-30)\°`

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:

`m\angle B=(2(50)-30)\°\\\\m\angle B=(100-30)\°\\\\m\angle B=70\°`