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We have the equation m∠A + m∠B + m∠C = 180°.
Substituting the given values, we get 67° + (2x+20)° + x° = 180°.
Combining like terms, we have 3x + 87° = 180°.
Subtracting 87° from both sides, we get 3x = 93°.
Dividing both sides by 3, we get x = 31°.
Therefore, the measure of ∠B is (2x+20)° = 2(31°) + 20° = 82°.
The measure of ∠B is 82°.