There are angles whose measures add to 180° . Their measures are: m∠A=67°, m∠B=(2x+20)°, and m∠C=x°. What is the measure of ∠B?(1 point)
To find the measure of angle B, we need to set up an equation using the fact that the measures of the angles A, B, and C add up to 180°.
m∠A + m∠B + m∠C = 180°
Substituting the given values:
67° + (2x + 20)° + x° = 180°
Combining like terms:
67° + 2x + 20° + x° = 180°
Simplifying:
87° + 3x° = 180°
Subtracting 87° from both sides:
3x° = 93°
Dividing both sides by 3:
x° = 31°
Now we can find the measure of angle B:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°
Therefore, the measure of ∠B is 82°.