To find the measure of angle \( \angle B \), we start by using the fact that the measures of angles \( m\angle A \), \( m\angle B \), and \( m\angle C \) add up to 180°.
Given:
- \( m\angle A = 67° \)
- \( m\angle B = (2x + 20)° \)
- \( m\angle C = x° \)
We can set up the equation:
\[ m\angle A + m\angle B + m\angle C = 180° \]
Substituting the given values:
\[ 67° + (2x + 20)° + x° = 180° \]
Combining like terms gives:
\[ 67 + 2x + 20 + x = 180 \]
Which simplifies to:
\[ 87 + 3x = 180 \]
Next, we isolate \( 3x \):
\[ 3x = 180 - 87 \] \[ 3x = 93 \]
Now, we solve for \( x \):
\[ x = \frac{93}{3} = 31 \]
Now that we have \( x \), we can find \( m\angle B \):
\[ m\angle B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82° \]
Therefore, the measure of \( \angle B \) is \( \boxed{82°} \).
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