In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C . If m∠A=22° , write an equation that you can use to solve for m∠C. Please

Answer 1

Given that ∠A and ∠B are vertical angles, we know that their measures are equal. Therefore, if \( m∠A = 22° \), it follows that:

\[ m∠B = m∠A = 22° \]

Additionally, since ∠B is complementary to ∠C, we can use the property of complementary angles which states that the sum of two complementary angles is 90 degrees:

\[ m∠B + m∠C = 90° \]

Substituting \( m∠B \) with 22° gives us:

\[ 22° + m∠C = 90° \]

To find an equation that you can use to solve for \( m∠C \), we can rearrange this equation:

\[ m∠C = 90° - 22° \]

Thus, the equation you can use to solve for \( m∠C \) is:

\[ m∠C = 90° - m∠B \]

Specifically, substituting the known measure:

\[ m∠C = 90° - 22° \]

So you have the equation:

\[ m∠C = 90° - 22° \]