To find the measure of \(\angle B\), we need to set up an equation based on the information given about the angles. We know that the sum of the angles is \(180^\circ\):
\[ m∠A + m∠B + m∠C = 180° \]
Given:
- \(m∠A = 67°\)
- \(m∠B = (2x + 20)°\)
- \(m∠C = x°\)
Substituting in these values, we have:
\[ 67° + (2x + 20)° + x° = 180° \]
Combining like terms:
\[ 67° + 20° + 2x + x = 180° \] \[ 87° + 3x = 180° \]
Now, isolate \(x\) by subtracting \(87°\) from both sides:
\[ 3x = 180° - 87° \] \[ 3x = 93° \]
Now, divide by 3:
\[ x = \frac{93°}{3} = 31° \]
Now that we found \(x\), we can substitute back to find \(m∠B\):
\[ m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82° \]
Thus, the measure of \(\angle B\) is:
\[ \boxed{82°} \]
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