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 .(2 points)

Question

Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.

Answer 1

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

Since ∠B is a complementary angle with ∠C, the sum of their measures is 90°. So, m∠B + m∠C = 90°.

Substitute m∠B = 22° into the equation:

22° + m∠C = 90°

Solve for m∠C:

m∠C = 90° - 22°
m∠C = 68°

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