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 31° 31 degrees 62° 62 degrees 180° 180 degrees
Based on the given information, we know that the sum of the angle measures is 180°. Therefore, we can set up the equation:
m∠A + m∠B + m∠C = 180
Substituting the given values:
67 + (2x + 20) + x = 180
Combine like terms and solve for x:
3x + 87 = 180
3x = 93
x = 31
Now that we have found the value of x, we can substitute it back into the equation to find m∠B:
m∠B = 2x + 20
m∠B = 2(31) + 20
m∠B = 62 + 20
m∠B = 82
Therefore, the measure of ∠B is 82°.