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
Since ∠A and ∠B are complementary, ∠A + ∠B = 90°.
Since ∠A and ∠B form a straight line with ∠C, ∠A + ∠C + ∠B = 180°.
Substituting the values, we have:
x + 90° + 2x = 180°
Combining like terms, we have:
3x + 90° = 180°
Subtracting 90° from both sides, we have:
3x = 90°
Dividing both sides by 3, we have:
x = 30°
Thus, the measure of ∠B is 2x = 2(30°) = 60°. Answer: \boxed{60}.