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 30° 30 degrees 90° 90 degrees 180° 180 degrees 60°
To find the measure of ∠B, we know that ∠A and ∠B are complementary, meaning their measures add up to 90 degrees. Since ∠A is given as x°, and ∠B is given as 2x°, we can set up the equation:
x° + 2x° = 90°
Combine like terms:
3x° = 90°
Divide both sides by 3:
x° = 30°
Since ∠B is given as 2x°, we can substitute x° with 30°:
∠B = 2(30°) = 60°
Therefore, the measure of ∠B is 60°.