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)
31°
82°
180°
62°
To find the measure of ∠B, we can use the fact that the sum of the measures of all three angles in a triangle is 180°.
So, we can write the equation: ∠A + ∠B + ∠C = 180°.
Substituting the given measures, we have:
67° + (2x + 20)° + x° = 180°.
Combining like terms, we get:
3x + 87 = 180.
Subtracting 87 from both sides, we have:
3x = 93.
Dividing both sides by 3, we get:
x = 31.
Now we can find the measure of ∠B:
∠B = 2x + 20 = 2(31) + 20 = 82.
Therefore, the measure of ∠B is 82°. Answer: \boxed{82}.