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 \( A \) ?

To find the measures of angles \( A \) and \( B \) that are complementary, we know that: \[ A + B = 90 \] Since angle \( A \) is 5 times the size of angle \( B \), we can write: \[ A = 5B \] Now, let's substitute the expression for \( A \) into the first equation: \[ 5B + B = 90 \] This simplifies to: \[ 6B = 90 \] Now, divide both sides by 6: \[ B = 15 \] Now, substitute \( B \) back to find \( A \): \[ A = 5B = 5 \times 15 = 75 \] Therefore, the measure of angle \( A \) is \( 75\) degrees. Learning about complementary angles can lead to some fascinating discoveries! Did you know that complementary angles are not just limited to two dimensions? They can also have implications in fields such as architecture, where angles are designed to create visually appealing structures or optimize space use. If you're looking to strengthen your skills in solving angle problems, try drawing diagrams! Visualizing the problem by sketching the angles can make relationships clearer and help avoid mistakes. Don't forget to double-check your equations to ensure accuracy; it's a common misstep to accidentally swap variable assignments or forget the complementary nature of the angles.