in a diagram ∠A and ∠B are vertical angles and ∠B is a complementary angle with ∠C if m∠A = 22 degrees write an equation that you can use to solve for m∠C

Answer 1

To solve for \( m\angle C \), we can use the relationships between the angles given in the problem.

1. Since \( \angle A \) and \( \angle B \) are vertical angles, they are equal: \[ m\angle A = m\angle B \]

2. Given that \( m\angle A = 22^\circ \), we have: \[ m\angle B = 22^\circ \]

3. Since \( \angle B \) and \( \angle C \) are complementary angles, this means that their measures add up to \( 90^\circ \): \[ m\angle B + m\angle C = 90^\circ \]

Now, substituting the measure of \( \angle B \) into the complementary angle equation: \[ 22^\circ + m\angle C = 90^\circ \]

To solve for \( m\angle C \), we can rearrange the equation: \[ m\angle C = 90^\circ - 22^\circ \]

Thus, we have: \[ m\angle C = 68^\circ \]

So, the equation to use for \( m\angle C \) is: \[ m\angle C = 90^\circ - m\angle B \] which can be explicitly written as: \[ m\angle C = 90^\circ - 22^\circ \] to find that \( m\angle C = 68^\circ \).