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 62° 62 degrees 31° 31 degrees 82° 82 degrees 180°
To find the measure of ∠B, we need to set up an equation using the fact that the sum of the measures of the angles is equal to 180°.
m∠A + m∠B + m∠C = 180°
Substituting the given values:
67° + (2x + 20)° + x° = 180°
Combining like terms:
67° + 2x + 20° + x° = 180°
3x + 87° = 180°
Subtracting 87° from both sides:
3x = 93°
Dividing both sides by 3:
x = 31°
Now that we have the value of x, we can substitute it back into the expression for ∠B to find its measure:
m∠B = 2x + 20°
= 2(31°) + 20°
= 82°
Therefore, the measure of ∠B is 82°.