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.

Question

seventh grader level please.

Answer 1

Since ∠A and ∠B are vertical angles, they are equal. So, we have:

\( m∠A = m∠B \)

Given that \( m∠A = 22° \), we can say:

\( m∠B = 22° \)

We also know that ∠B is complementary to ∠C. This means that the measure of ∠B plus the measure of ∠C adds up to 90°. We can write this relationship as an equation:

\( m∠B + m∠C = 90° \)

Now, substitute \( m∠B \) with 22°:

\( 22° + m∠C = 90° \)

This is the equation you can use to solve for \( m∠C \). To find \( m∠C \), you would subtract 22° from both sides:

\( m∠C = 90° - 22° \)

Now you can calculate \( m∠C \).