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
180°
180 degrees
30°
∠A and ∠B are complementary, which means they add up to 90°. Since ∠A and ∠B form a straight line with ∠C, they must add up to 180°.
So, x° + 2x° + 90° = 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°
Since ∠B is equal to 2x°, we have:
∠B = 2(30°)
∠B = 60°
Therefore, the measure of ∠B is 60°.