Write an equation that can be used to solve the problem. Find the solution to the problem. Angles \( A \) and \( B \) are complementary angles. Determine the measures of angles \( A \) and \( B \) if angle \( A \) is 5 times the size of angle \( B \). What is the measure of angle \( A \) ? \( 75^{\circ} \) What is the measure of angle \( B \) ? \( \square^{\circ} \)

To solve the problem of finding the measures of complementary angles \( A \) and \( B \) where angle \( A \) is 5 times the size of angle \( B \), follow these steps: ### Step 1: Define the Relationship Since angles \( A \) and \( B \) are complementary, their measures add up to \( 90^\circ \): \[ A + B = 90^\circ \] Given that angle \( A \) is 5 times the size of angle \( B \): \[ A = 5B \] ### Step 2: Substitute and Formulate the Equation Substitute the expression for \( A \) from the second equation into the first equation: \[ 5B + B = 90^\circ \] ### Step 3: Solve for \( B \) Combine like terms: \[ 6B = 90^\circ \] \[ B = \frac{90^\circ}{6} = 15^\circ \] ### Step 4: Find the Measure of \( A \) Now, substitute the value of \( B \) back into the equation \( A = 5B \): \[ A = 5 \times 15^\circ = 75^\circ \] ### Final Answer - **Measure of angle \( A \):** \( 75^\circ \) - **Measure of angle \( B \):** \( 15^\circ \) \[ \boxed{A = 75^\circ \quad \text{and} \quad B = 15^\circ} \]