The complement of an angle measuring x is 5 x . Solve for x . A. \( 18^{\circ} \) B. \( 10^{\circ} \) C. \( 15^{\circ} \) D. \( 12^{\circ} \)

To find the value of \( x \), we know that the complement of an angle is given by \( 90^\circ - x \). Given that the complement equals \( 5x \), we can set up the equation: \[ 90^\circ - x = 5x \] Now, we add \( x \) to both sides: \[ 90^\circ = 6x \] Dividing both sides by 6 gives us: \[ x = 15^\circ \] Thus, the answer is C. \( 15^{\circ} \). Now for a bit of trivia: Did you know that the concept of complementary angles dates back to ancient Greek mathematics? Mathematicians like Euclid explored the relationships between angles, forming the basis of much of geometry today! And speaking of angles, one common mistake when solving angle problems is to forget that the total of complementary angles must always add up to \( 90^\circ \). Keeping track of this simple principle can save you from unnecessary errors!