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
60°
60 degrees
30°
30 degrees
90°
90 degrees
180°
To find the measure of angle B, we can use the fact that the sum of angles in a straight line is 180°.
Since angle A and angle B are complementary (meaning they add up to 90°) and they form a straight line with angle C (which is 90°), angle A, angle B, and angle C must add up to 180°.
Therefore, we have the equation:
x° + 2x° + 90° = 180°
Simplifying this equation, we get:
3x° + 90° = 180°
Subtracting 90° from both sides, we have:
3x° = 90°
Dividing both sides by 3, we find:
x° = 30°
Since angle B is 2x°, we can substitute x° with 30° to find the measure of angle B:
B = 2(30°) = 60°
Therefore, the measure of angle B is 60°.