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
31°
31 degrees
62°
62 degrees
82°
82 degrees
180°
To find the measure of ∠B, we can use the fact that the sum of the measures of the angles in a triangle is always 180°.
So, we can set up the equation:
m∠A + m∠B + m∠C = 180°
67 + (2x+20) + x = 180
Simplifying the equation, we combine like terms:
3x + 87 = 180
Subtracting 87 from both sides:
3x = 93
Dividing both sides by 3:
x = 31
Now that we have found the value of x, we can substitute it back into the expression for ∠B:
m∠B = 2x + 20 = 2(31) + 20 = 62 + 20 = 82
Therefore, the measure of ∠B is 82 degrees.