There are angles whose measures add to 180°

Question

. Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ?(1 point)
Responses

62°
62 degrees

31°
31 degrees

82°
82 degrees

180°

Answer 1

We are given that the sum of the measures of angle A, angle B, and angle C is 180°. So we can set up the equation:

m∠A + m∠B + m∠C = 180°

Substituting the given measures:

67° + (2x + 20)° + x° = 180°

Combining like terms:

3x + 87° = 180°

Subtracting 87° from both sides:

3x = 93°

Dividing both sides by 3:

x = 31°

Therefore, the measure of angle B is:

m∠B = 2x + 20° = 2(31°) + 20° = 82°

So the correct answer is 82°.