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, their measures add up to 90°.
Let's set up an equation to find ∠B:
∠A + ∠B = 90°
Substituting the given values:
x° + (2x)° = 90°
Combining like terms:
3x° = 90°
Dividing both sides by 3:
x = 30°
Now we can find the measure of ∠B:
∠B = 2x = 2(30°) = 60°
Therefore, the measure of ∠B is 60°.