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 ?

Question

Responses:
82°
31°
62°
180°

Answer 1

To find the measure of angle B, we can use the fact that the sum of the measures of the angles in a triangle is 180°.

Therefore, we have 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 that we have the value of x, we can substitute it back into the equation to find the measure of angle B:

m∠B = (2x + 20) = (2*31 + 20) = 82

Therefore, the measure of angle B is 82°.