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 . step-by-step

Answer 1

To write an equation to solve for \( m∠C \), we will follow these steps:

Step 1: Understand Vertical Angles

Since \( ∠A \) and \( ∠B \) are vertical angles, they are equal. This means: \[ m∠A = m∠B \] Given: \[ m∠A = 22° \] Thus, we have: \[ m∠B = 22° \]

Step 2: Understand Complementary Angles

Next, we know that \( ∠B \) and \( ∠C \) are complementary angles. This means that their measures add up to \( 90° \): \[ m∠B + m∠C = 90° \]

Step 3: Substitute Known Values

We already know that \( m∠B = 22° \). Therefore, we can substitute this value into the complementary angle equation: \[ 22° + m∠C = 90° \]

Step 4: Write the Equation to Solve for \( m∠C \)

Now, we need to isolate \( m∠C \) in the equation: \[ m∠C = 90° - 22° \]

Step 5: Simplify the Equation

Now simplify to find \( m∠C \): \[ m∠C = 68° \]

So the equation you can use to find \( m∠C \) is: \[ m∠C = 90° - m∠B \] Or, explicitly with the values: \[ m∠C = 90° - 22° \]