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 180° 180 degrees 31° 31 degrees
To find the measure of ∠B, we need to solve the equation:
m∠A + m∠B + m∠C = 180°
Substituting in the given values, we have:
67° + (2x + 20)° + x° = 180°
Combining like terms:
3x + 87° = 180°
Subtracting 87° from both sides:
3x = 93°
Dividing both sides by 3:
x = 31°
Substituting this value back into the equation for ∠B:
m∠B = 2x + 20° = 2(31°) + 20° = 82°
Therefore, the measure of ∠B is 82 degrees.