Name Complementary and Supplementary Angles (continued)

Complementary and supplementary angles are two important concepts in geometry. 1. **Complementary Angles**: Two angles are complementary if the sum of their measures is \(90^\circ\). For example, if one angle measures \(30^\circ\), its complement would measure \(60^\circ\) because \(30^\circ + 60^\circ = 90^\circ\). 2. **Supplementary Angles**: Two angles are supplementary if the sum of their measures is \(180^\circ\). For instance, if one angle measures \(110^\circ\), its supplement would measure \(70^\circ\) because \(110^\circ + 70^\circ = 180^\circ\). ### Examples: - **Complementary Angles**: - \(45^\circ\) and \(45^\circ\) are complementary because \(45^\circ + 45^\circ = 90^\circ\). - \(20^\circ\) and \(70^\circ\) are complementary because \(20^\circ + 70^\circ = 90^\circ\). - **Supplementary Angles**: - \(90^\circ\) and \(90^\circ\) are supplementary because \(90^\circ + 90^\circ = 180^\circ\). - \(130^\circ\) and \(50^\circ\) are supplementary because \(130^\circ + 50^\circ = 180^\circ\). ### Key Points: - Complementary angles can be adjacent (next to each other) or non-adjacent. - Supplementary angles can also be adjacent or non-adjacent. - The concepts are often used in various applications, including trigonometry, architecture, and design. If you have specific problems or examples related to complementary and supplementary angles that you would like to solve or discuss, please provide them!