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 180° 180 degrees 60° 60 degrees 90° 90 degrees 30°
We know that angles ∠A and ∠B are complementary, meaning that their measures add up to 90 degrees. Since ∠A measures x degrees, and ∠B measures 2x degrees, we can write an equation: x + 2x = 90. Combining like terms, we get 3x = 90. Dividing both sides by 3, we find that x = 30. Therefore, ∠B measures 2x = 2(30) = 60 degrees. So, the measure of ∠B is 60°.
