In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C. If m∠A=x°, m∠B=(2x)°, and m∠C=90°, what is the measure of ∠B?(1 point)
Responses
180°
180 degrees
60°
60 degrees
30°
30 degrees
90°
The measure of ∠B can be found by setting up an equation using the fact that the sum of the measures of ∠A and ∠B is equal to 180° (since they are complementary and form a straight line).
m∠A + m∠B = 180°
Substituting the given values:
x° + (2x)° = 180°
Combining like terms:
3x° = 180°
Solving for x:
x = 180°/3
x = 60°
Therefore, the measure of ∠B is (2x)° = 2(60°) = 120°.
The correct answer is 120°.