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)

Question

Responses

60°
60 degrees

30°
30 degrees

180°
180 degrees

90°

Answer 1

In the given problem, we know the following:

1. Angles A and B are complementary, which means that their measures add up to 90 degrees: \[ m∠A + m∠B = 90° \]

2. You are given that \( m∠A = x° \) and \( m∠B = 2x° \).

Substituting the expressions for angles A and B into the complementary angle equation, we get: \[ x + 2x = 90° \] \[ 3x = 90° \] Dividing both sides by 3: \[ x = 30° \]

Now, we can find the measure of \( m∠B \): \[ m∠B = 2x = 2(30°) = 60° \]

Thus, the measure of ∠B is 60°.