In a diagram, ∠A

Question

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
.(2 points)

Answer 1

To solve for \( m\angle C \), we can start by using the information provided about the angles.

1. Since \( \angle A \) and \( \angle B \) are vertical angles, they are equal. Therefore: \[ m\angle B = m\angle A = 22^\circ \]

2. We know that \( \angle B \) is complementary to \( \angle C \). By definition of complementary angles: \[ m\angle B + m\angle C = 90^\circ \]

3. Substituting \( m\angle B \) into the equation gives us: \[ 22^\circ + m\angle C = 90^\circ \]

Now you can solve for \( m\angle C \): \[ m\angle C = 90^\circ - 22^\circ \]

Thus, the equation to solve for \( m\angle C \) is: \[ m\angle C = 90^\circ - 22^\circ \]