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 90° 90 degrees 60° 60 degrees 180° 180 degrees 30°
We know that the sum of the measures of two complementary angles is 90 degrees. Since ∠A and ∠B are complementary angles, we have:
m∠A + m∠B = 90°
Substituting the given values, we have:
x + 2x = 90°
Combining like terms, we get:
3x = 90°
Dividing both sides by 3, we get:
x = 30°
Since ∠B is 2 times the measure of ∠A, we have:
m∠B = 2(30°) = 60°
Therefore, the measure of ∠B is 60 degrees.