To find the measure of angle B, we can start by setting up the equation based on the information given. The sum of the angles is 180°. We have:
\[ m∠A + m∠B + m∠C = 180° \]
Substituting the given measures:
\[ 67° + (2x + 20)° + x° = 180° \]
Now, we simplify the equation:
\[ 67 + 2x + 20 + x = 180 \]
Combine like terms:
\[ 87 + 3x = 180 \]
Now, isolate \(3x\):
\[ 3x = 180 - 87 \]
\[ 3x = 93 \]
Now, divide by 3:
\[ x = 31 \]
Now we will substitute \(x\) back into the expression for angle B:
\[ m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82° \]
Thus, the measure of angle B is 82°.