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 ? Please

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 values into the equation:

\[ x + 2x = 90° \]

This simplifies to:

\[ 3x = 90° \]

Now, to find \( x \), we divide both sides by 3:

\[ x = \frac{90°}{3} = 30° \]

We have found \( m∠A \):

\[ m∠A = x = 30° \]

Next, we calculate \( m∠B \):

\[ m∠B = 2x = 2(30°) = 60° \]

Therefore, the measure of \( ∠B \) is

\[ \boxed{60°} \]