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 can use to solve for m∠C.

1 answer

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

Because ∠B is a complementary angle with ∠C, we know that m∠B + m∠C = 90.

Substitute the known value of m∠B into the equation:

22 + m∠C = 90

Rearrange the equation to solve for m∠C:

m∠C = 90 - 22
m∠C = 68

Therefore, m∠C = 68.