Angle Pairs Unit Test17 of 17 17 of 17 ItemsQuestionIn 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)BoldItalicUnderlineIncrease indentDecrease indentFormula keypadUndoRedo Math Short Answer Rubric (2 points)Points Awarded Criteria2 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, \( m∠A = m∠B \).

Given \( m∠A = 22° \), we have:
\[ m∠B = 22°. \]

Since ∠B is complementary to ∠C, the sum of their measures is 90°. Therefore, we have:
\[ m∠B + m∠C = 90°.\]

Substituting \( m∠B = 22° \) into the equation, we get:
\[ 22° + m∠C = 90°.\]

To solve for \( m∠C \), we subtract 22° from both sides:
\[ m∠C = 90° - 22°. \]

This simplifies to:
\[ m∠C = 68°. \]

Therefore, the equation you can use to solve for \( m∠C \) is:
\[ 22° + m∠C = 90°. \]