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 ?

Answer 1

Since the sum of the angles is 180°, we can write the equation as:

m∠A + m∠B + m∠C = 180°

Substituting the given values, we have:

67° + (2x + 20)° + x° = 180°

Combining like terms, we get:

3x + 87° = 180°

Subtracting 87° from both sides gives:

3x = 93°

Dividing both sides by 3 gives:

x = 31°

Substituting this value back into m∠B = (2x + 20)°, we have:

m∠B = (2 * 31° + 20°)° = (62° + 20°)° = 82°

Therefore, the measure of ∠B is 82°.