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
30°
30 degrees
180°
180 degrees
60°
60 degrees
90°
To find the measure of ∠B, we need to use the fact that ∠A and ∠B are complementary, meaning they add up to 90 degrees.
We are given that m∠A = x° and m∠B = (2x)°. Since they are complementary, we can set up the equation:
x + 2x = 90
Combining like terms, we get:
3x = 90
To solve for x, we divide both sides of the equation by 3:
x = 90/3
Simplifying the right side, we find:
x = 30
Therefore, the measure of ∠B is 2x, which is equal to 2(30) = 60 degrees.
So, the correct answer is 60°.