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 ∠B?

Answer 1

Let's use the fact that the measure of the angles must add up to 180 degrees.

m ∠A + m ∠B + m ∠C = 180

Substituting the given values:

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

Now we can substitute this value back into the equation to find the measure of angle ∠B:

m ∠B = 2(31) + 20

m ∠B = 62 + 20

m ∠B = 82

Therefore, the measure of angle ∠B is 82 degrees.