Question

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) Responses 31° 31 degrees 62° 62 degrees 180° 180 degrees 82°

Answer 1

We have the equation m∠A + m∠B + m∠C = 180°.

Substituting the given values, we get 67° + (2x+20)° + x° = 180°.

Combining 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°.

Therefore, the measure of ∠B is (2x+20)° = 2(31°) + 20° = 82°.

The measure of ∠B is 82°.