To find the measure of ∠B, we need to set up an equation based on the given information about the angles. The problem states that:
\[ m∠A + m∠B + m∠C = 180° \]
Given:
- \( m∠A = 67° \)
- \( m∠B = (2x + 20)° \)
- \( m∠C = x° \)
Now we can substitute these values into the equation:
\[ 67° + (2x + 20)° + x° = 180° \]
Combining like terms:
\[ 67 + 2x + 20 + x = 180 \]
This simplifies to:
\[ 3x + 87 = 180 \]
Now, subtract 87 from both sides:
\[ 3x = 180 - 87 \] \[ 3x = 93 \]
Now, divide by 3:
\[ x = 31 \]
Now that we have \( x \), we can find the measure of \( m∠B \):
\[ m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82° \]
Thus, the measure of \( ∠B \) is:
\[ \boxed{82°} \]