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° 82 degrees
To find the measure of ∠B, we need to set up an equation by the fact that the sum of the measures of the angles is 180°.
m∠A + m∠B + m∠C = 180°
Plugging in the given measures:
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°
Therefore, the measure of ∠B is (2x + 20)°, plug in the value of x:
∠B = 2(31°) + 20°
∠B = 62° + 20°
∠B = 82°
So, the measure of ∠B is 82°.