n 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 180° 180 degrees 60° 60 degrees 90°
Since ∠A and ∠B are complementary angles, we know that ∠A + ∠B = 90°.
We also know that ∠C = 90°.
Since ∠A + ∠B = 90°, and ∠C = 90°, the sum of all the angles is 180° (90° + 90° = 180°).
This means that ∠A + ∠B + ∠C = 180°.
Since ∠A + ∠B + ∠C = 180°, we can substitute the given values to get:
x + 2x + 90° = 180°
Combining like terms, we get:
3x + 90° = 180°
Subtracting 90 from both sides, we get:
3x = 90°
Dividing both sides by 3, we get:
x = 30°
Since ∠B is 2 times ∠A, we can find ∠B by multiplying the value of ∠A by 2:
∠B = 2 * x
∠B = 2 * 30°
∠B = 60°
Therefore, the measure of ∠B is 60°.