In a geometric diagram, ∠A

Question

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°

Answer 1

Since angles A and B are complementary, their measures must add up to 90°. According to the given information:

• \( m∠A = x° \)
• \( m∠B = 2x° \)

Since they are complementary: \[ m∠A + m∠B = 90° \] Substituting the expressions for angles A and B: \[ x + 2x = 90° \] This simplifies to: \[ 3x = 90° \] Now, solve for \( x \): \[ x = \frac{90°}{3} = 30° \]

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

Therefore, the measure of \( ∠B \) is 60°.