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

180°
180 degrees

60°
60 degrees

90°
90 degrees

30°

Answer 1

Since angles A and B are complementary, we know that:

\[ m∠A + m∠B = 90° \]

Given that \( m∠A = x° \) and \( m∠B = 2x° \), we can substitute these into the equation:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

Now, divide both sides by 3:

\[ x = 30° \]

Now that we have the measure of angle A:

\[ m∠A = x = 30° \]

Next, we find the measure of angle B:

\[ m∠B = 2x = 2(30°) = 60° \]

Therefore, the measure of angle B is:

\[ \boxed{60°} \]