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 ?
We know that the sum of the measures of the angles of a triangle is 180°. Therefore, we can set up the equation:
m∠A + m∠B + m∠C = 180°
Substituting the given measures:
67° + (2x+20)° + x° = 180°
Combine like terms:
3x + 87° = 180°
Subtract 87° from both sides:
3x = 93°
Divide both sides by 3:
x = 31°
Now we can find the measure of ∠B:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°
Therefore, the measure of ∠B is 82°.