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 ?
Since the sum of the angles is 180°, we can write the equation as:
m∠A + m∠B + m∠C = 180°
Substituting the given values, we have:
67° + (2x + 20)° + x° = 180°
Combining like terms, we get:
3x + 87° = 180°
Subtracting 87° from both sides gives:
3x = 93°
Dividing both sides by 3 gives:
x = 31°
Substituting this value back into m∠B = (2x + 20)°, we have:
m∠B = (2 * 31° + 20°)° = (62° + 20°)° = 82°
Therefore, the measure of ∠B is 82°.