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 ∠B, we need to solve for x. Since the sum of the angles in a triangle is 180°, we have the equation:
m∠A + m∠B + m∠C = 180°
Substituting the given values, we have:
67° + (2x+20)° + x° = 180°
Combining like terms, we get:
67° + 2x + 20° + x° = 180°
Collecting 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°
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°.