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

82°
82 degrees

62°
62 degrees

31°
31 degrees

180°

To find the measure of angle B, we can set up the equation:

m∠A + m∠B + m∠C = 180°

Substituting in the given measures, we have:

67° + (2x+20)° + x° = 180°

Combining like terms, we have:

3x + 87° = 180°

Subtracting 87° from both sides:

3x = 93°

Divide both sides by 3:

x = 31°

Now we can find the measure of angle B:

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

So, the measure of angle B is 82°.