Justify Conclusions A student said that a pair of complementary angles cannot also be adjacent angles. Is the student correct? Explain. Support your answer with a drawing.

To determine whether a pair of complementary angles can also be adjacent angles, let's first define the terms: 1. **Complementary Angles**: Two angles are complementary if the sum of their measures is \(90^\circ\). 2. **Adjacent Angles**: Two angles are adjacent if they share a common vertex and a common side, and do not overlap. Now, let's analyze the situation: - If we have two angles, \(A\) and \(B\), that are complementary, we can express this relationship mathematically as: \[ A + B = 90^\circ \] - If these angles are also adjacent, they will share a common vertex and a common side. ### Drawing To visualize this, we can draw two angles that are complementary and adjacent: 1. Draw a horizontal line segment (let's call it line \(AB\)). 2. At point \(A\), draw angle \(A\) such that it opens upwards. 3. At point \(A\) again, draw angle \(B\) such that it opens to the right. In this configuration, angles \(A\) and \(B\) share the vertex \(A\) and the side \(AB\). ### Conclusion Since we can find a configuration where two angles are both complementary (their measures add up to \(90^\circ\)) and adjacent (they share a common vertex and side), the student's statement is incorrect. Thus, complementary angles can indeed be adjacent angles. To summarize: - The student is incorrect. - Complementary angles can be adjacent, as demonstrated by the drawing and the definitions provided.