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 82° 82 degrees 62° 62 degrees 31° 31 degrees
The measure of ∠B is 62°.
Given that m∠A = 67°, m∠B = (2x + 20)°, and m∠C = x°, we know that the sum of the angles in a triangle is 180°.
So, m∠A + m∠B + m∠C = 180°.
Substitute the given values:
67° + (2x + 20)° + x° = 180°
67° + 2x + 20° + x = 180°
Combine like terms:
3x + 87° = 180°
Subtract 87° from both sides:
3x = 93°
Divide by 3:
x = 31°
Now that we have found the value of x, we can find the measure of ∠B:
m∠B = 2x + 20
m∠B = 2(31) + 20
m∠B = 62 + 20
m∠B = 82°
Therefore, the measure of ∠B is 82°.