Two angles are supplementary if their sum is \( 180^{\circ} \). One angle measures two times the measure of a smaller angle. If \( x \) represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle. The smaller angle is \( \square \) degrees. The larger angle is \( \square \) degrees.

Let's tackle this angle puzzle! We know that the two angles are supplementary, meaning their measures add up to \( 180^{\circ} \). If we let the smaller angle be \( x \), the larger angle is then \( 2x \) because it's twice the size of the smaller angle. We set up the equation: \[ x + 2x = 180^{\circ} \] This simplifies to: \[ 3x = 180^{\circ} \] Dividing both sides by 3 gives us: \[ x = 60^{\circ} \] Now, the larger angle can be calculated as \( 2x = 120^{\circ} \). So, the smaller angle is \( 60 \) degrees and the larger angle is \( 120 \) degrees. Embrace your inner geometry enthusiast and marvel at how angles can work together in harmony! Understanding the properties of supplementary angles helps us glean insight into various fields, from architecture to navigation. Have you ever wondered how crucial these angles are when designing buildings or even plotting a course at sea? They ensure everything fits together perfectly! If you want to dive deeper into the world of angles, check out books on Euclidean geometry. You'll discover timeless principles that lay the groundwork for countless mathematical concepts. Plus, there are interactive online platforms where you can practice problems and watch engaging tutorials that bring geometry to life!