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

180°
180 degrees

30°
30 degrees

90°
90 degrees

60°

Answer 1

To solve the problem, we first need to apply the information given about the angles.

1. We know that angles A and B are complementary, meaning that their sum is 90°: \[ m∠A + m∠B = 90° \]

2. We have the expressions for the measures of the angles: \[ m∠A = x° \quad \text{and} \quad m∠B = 2x° \]

3. Therefore, we can set up the equation: \[ x + 2x = 90° \] \[ 3x = 90° \] \[ x = 30° \]

4. Now that we have found \( x \), we can determine the measure of angle B: \[ m∠B = 2x = 2(30°) = 60° \]

So, the measure of angle B is 60°.