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 ?

Answer 1

We know that the sum of the measures of angles A, B, and C must add up to 180°.

So, 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, we have 3x = 180° - 87°.

Simplifying, we get 3x = 93°.

Dividing both sides by 3, we find x = 31°.

Substituting this value back into the expression for m∠B, we have m∠B = 2x + 20° = 2(31°) + 20° = 82°.

So, the measure of ∠B is 82°.