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
180°
180 degrees
62°
62 degrees
82°
82 degrees
31°
31 degrees
To find the measure of ∠B, we can set up an equation since the sum of the measures of the angles is equal to 180°.
m∠A + m∠B + m∠C = 180°
Substituting the given measures of ∠A and ∠C:
67° + (2x + 20)° + x° = 180°
Simplifying the equation:
67° + 2x + 20° + x° = 180°
3x + 87° = 180°
3x = 180° - 87°
3x = 93°
x = 93° / 3
x = 31°
Now, substituting the value of x back into the measure of ∠B:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°
Therefore, the measure of ∠B is 82°.