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
60°
60 degrees
90°
90 degrees
30°
30 degrees
180°
We know that the sum of the angles in a straight line is equal to 180 degrees. Since ∠C is 90 degrees, and ∠A and ∠B are complementary, the sum of ∠A and ∠B is also 90 degrees.
Therefore, we have the equation:
x + 2x = 90
Combining like terms:
3x = 90
Dividing both sides by 3:
x = 30
Since we are looking for the measure of ∠B, which is 2x, we can substitute x = 30 into the equation:
2(30) = 60
Therefore, the measure of ∠B is 60 degrees.