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 30° 30 degrees 180°
Since ∠A and ∠B are complementary, we know that their measures sum up to 90°. That means:
∠A + ∠B = 90°
We also know that ∠C is a straight angle, which means it measures 180°. Since ∠C is the sum of ∠A and ∠B, we can write:
∠A + ∠B = ∠C
Since ∠C measures 90°, we have:
∠A + ∠B = 90°
Plugging this into the previous equation, we have:
90° = 90°
This shows that the measure of ∠B is 90°.