To determine the measure of ∠B, we start by using the information that the sum of angles A, B, and C is 180°. We are given:
- m∠A = 67°
- m∠B = (2x + 20)°
- m∠C = x°
We can set up the equation based on the sum of the angles:
\[ m∠A + m∠B + m∠C = 180° \]
Substituting in the known values:
\[ 67° + (2x + 20)° + x° = 180° \]
Combining like terms:
\[ 67° + 2x + 20 + x = 180° \]
\[ 67° + 20° = 87° \]
So, we simplify to:
\[ 87° + 3x = 180° \]
Next, we solve for x by subtracting 87° from both sides:
\[ 3x = 180° - 87° \]
\[ 3x = 93° \]
Now, dividing by 3 gives us:
\[ x = 31° \]
Now that we have the value of x, we can find m∠B:
\[ m∠B = 2x + 20° \]
Substituting x = 31°:
\[ m∠B = 2(31) + 20 = 62 + 20 = 82° \]
Thus, the measure of ∠B is:
82°