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 .

Answer 1

Since ∠A and ∠B are vertical angles, they are congruent. Therefore, m∠A = m∠B = 22°.

Also, ∠B and ∠C are complementary angles. This means that the sum of their measures is 90°. So, m∠B + m∠C = 90°.

Substituting the value, m∠B = 22°, we get 22 + m∠C = 90.

Therefore, the equation to solve for m∠C is 22 + m∠C = 90.