Question

There are angles whose measures add to 180° . Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ?(1 point) Responses 180° 180 degrees 31° 31 degrees 62° 62 degrees 82°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of ∠B, we need to set up an equation using the given information that the sum of the measures of all three angles is 180°:

m∠A + m∠B + m∠C = 180°
67° + (2x+20)° + x° = 180°
67° + 2x + 20° + x = 180°
3x + 87° = 180°
3x = 93°
x = 31°

Now that we have found the value of x, we can plug it back into the expression for the measure of ∠B:

m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°

Therefore, the measure of ∠B is 82°.