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
82°
82 degrees
180°
180 degrees
62°
62 degrees
To find the measure of ∠B, we need to set up an equation using the fact that the measures of the angles add up to 180°.
m∠A + m∠B + m∠C = 180°
Substituting the given measures:
67° + (2x+20)° + x° = 180°
Simplifying:
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°
Substituting x=31° back into the equation for ∠B:
m∠B = 2x + 20°
m∠B = 2(31°) + 20°
m∠B = 62° + 20°
m∠B = 82°
Therefore, the measure of ∠B is 82°. Answer: 82 degrees