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)

Answer 1

To find the measure of angle B, we need to set up an equation using the fact that the measures of the angles A, B, and C add up to 180°.

m∠A + m∠B + m∠C = 180°

Substituting the given values:

67° + (2x + 20)° + x° = 180°

Combining like terms:

67° + 2x + 20° + x° = 180°

Simplifying:

87° + 3x° = 180°

Subtracting 87° from both sides:

3x° = 93°

Dividing both sides by 3:

x° = 31°

Now we can find the measure of angle B:

m∠B = 2x + 20°

m∠B = 2(31°) + 20°

m∠B = 62° + 20°

m∠B = 82°

Therefore, the measure of ∠B is 82°.