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, we can set up the equation based on the information given. Since angles \( A \) and \( B \) are complementary, we have \( A + B = 90^\circ \). Given that \( A = 5B \), we can substitute to get \( 5B + B = 90^\circ \) or \( 6B = 90^\circ \). This gives us \( B = 15^\circ \). Therefore, \( A = 5B = 75^\circ \). So, to summarize: Angle \( A \) measures \( 75^\circ \) and angle \( B \) measures \( 15^\circ \). Now, let’s chat about the history of angles! Did you know that the concept of complementary angles dates back to ancient Greek mathematicians? They explored angles in relation to their properties, laying the groundwork for modern geometry! For those looking to sharpen their skills in trigonometry and geometry, consider diving into some math-centered games and puzzles! Websites that offer math riddles, angle-deduction games, and geometry challenges can really help solidify your understanding while keeping things fun.