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)
Responses
82°
82 degrees
31°
31 degrees
180°
180 degrees
62°
62 degrees
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To find the measure of angle B, we need to set up an equation using the fact that the sum of the measures of the angles is equal to 180 degrees:
m∠A + m∠B + m∠C = 180°
Substituting the given values:
67° + (2x+20)° + x° = 180°
Simplifying the equation:
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 that we have the value of x, we can find the measure of angle B:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 82°
Therefore, the measure of angle B is 82°.