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

82°
31°
180°
62

Answer 1

To find the measure of ∠B, we need to use the fact that the measures of the angles add up to 180°.

The sum of the measures of angles A, B, and C is:
m∠A + m∠B + m∠C = 180°

We know that m∠A = 67°, m∠B = (2x+20)°, and m∠C = x°.

Substituting these values into the equation:
67° + (2x+20)° + x° = 180°

Combining like terms:
3x + 87° = 180°

Subtracting 87° from both sides of the equation:
3x = 180° - 87°
3x = 93°

Dividing both sides by 3:
x = 93° / 3
x = 31°

So, the measure of ∠B is:
m∠B = 2x + 20°
= 2(31°) + 20°
= 62° + 20°
= 82°

Therefore, the correct answer is 82°.