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 180° 180 degrees 90°
From the information given, we know that ∠A and ∠B are complementary, which means they add up to 90°. Since ∠C is a right angle and forms a straight line with ∠A and ∠B, it means that ∠A and ∠B add up to 180°.
We also know that ∠A = x° and ∠B = 2x°.
So, x° + 2x° = 180°
Combining like terms, we get 3x° = 180°.
To solve for x, we divide both sides of the equation by 3:
x = 180° / 3 = 60°
Therefore, the measure of ∠B is 2x° = 2 * 60° = 120°.
The correct answer is 120°.